Micromorphology and diffusivity of filamentous fungal pellets ...

Technische Universität München

TUM School of Life Sciences

Lehrstuhl für Systemverfahrenstechnik

Following fungal features – Micromorphology anddiffusivity of filamentous fungal pellets revealed bythree-dimensional imaging and simulation

Stefan Schmideder

Vollständiger Abdruck der von der TUM School of Life Sciences der Technischen

Universität München zur Erlangung des akademischen Grades eines Doktors der

Ingenieurwissenschaften (Dr.-Ing.) genehmigten Dissertation.

Vorsitzender: Prof. Dr.rer.nat. Philipp Benz

Prüfer der Dissertation: 1. Prof. Dr.-Ing. Heiko Briesen

2. Prof. Dr.-Ing. Andreas Kremling

3. Prof. Dr. Peter J. Punt

Die Dissertation wurde am 01.04.2021 bei der Technischen Universität München

eingereicht und durch die TUM School of Life Sciences am 11.10.2021 angenommen.

Technische Universität München

TUM School of Life Sciences

Following fungal features – Micromorphology anddiffusivity of filamentous fungal pellets revealed bythree-dimensional imaging and simulation

Stefan Schmideder

Vollständiger Abdruck der von der TUM School of Life Sciences der Technischen

Universität München zur Erlangung des akademischen Grades eines Doktors der

Ingenieurwissenschaften (Dr.-Ing.) genehmigten Dissertation.

Vorsitzender: Prof. Dr.rer.nat. Philipp Benz

Prüfer der Dissertation: 1. Prof. Dr.-Ing. Heiko Briesen

2. Prof. Dr.-Ing. Andreas Kremling

3. Prof. Dr. Peter J. Punt

Die Dissertation wurde am 01.04.2021 bei der Technischen Universität München

eingereicht und durch die TUM School of Life Sciences am 11.10.2021 angenommen.

Abstract

Filamentous fungal biotechnology started in 1919 with the industrial production of citric acid

in Aspergillus niger. Today, more than 100 years later, it has emerged as a promising key tech-

nology for the transition from a petroleum-based economy into a bio-based circular economy.

Filamentous fungi in industrial applications are usually cultivated under submerged condi-

tions where their morphology strongly correlates with the productivity. In many processes,

dense hyphal agglomerates known as pellets are formed. Due to their size of up to several

millimeter and their dense hyphal network, the transport of nutrients and oxygen to the center

of pellets is diffusion-limited. This alters product formation. Although the inner structure

and the resulting diffusivity of pellets have a high impact on their productivity, they remained

largely unexplored. For example, there is no method to analyze the hyphal network, i.e., the

micromorphology, of whole pellets. In addition, correlations between the morphology and

the diffusive transport of nutrients through pellets are lacking in literature.

In this publication-based dissertation, three papers are embedded showing methods to ana-

lyze the morphology and diffusivity of filamentous fungal pellets . The first paper describes

techniques enabling the visualization and analysis of hyphal networks of whole pellets for

the first time. Based on X-ray microcomputed tomography (µCT) measurements and three-

dimensional (3D) image analysis, various morphological properties including the location of

tips, branches, and hyphal material can be investigated. In the second paper, the first ap-

proach of correlating 3D hyphal networks to diffusivity known until today is introduced. For

this purpose, diffusion computations were conducted through the structure of pellets gained

from µCT measurements. The third paper reveals a universal law for the diffusivity through

mycelial networks. This law is based on correlation analysis between diffusivities and struc-

tures of 66 µCT measured pellets originating from four filamentous fungi as well as 3125

Monte Carlo simulated pellets. Therein, the simulated pellets cover the broad morphological

range of filamentous fungi. Regardless of the detailed morphology gained from experiments

and simulations, the data showed that diffusivity follows a scaling law with respect to the

solid hyphal fraction.

The methods and findings of this thesis enable the analysis of the micromorphology and

the prediction of the diffusive mass transport of nutrients, oxygen, and secreted metabolites

within any filamentous fungal pellet. These achievements will open new paths towards tar-

geted morphological engineering of pellets to enhance productivities in fungal biotechnology.

i

Zusammenfassung

Die Biotechnologie filamentöser Pilze begann 1919 mit der industriellen Produktion von Zi-

tronensäure in Aspergillus niger. Heute, mehr als 100 Jahre später, ist sie ein Hoffnungs-

träger für den Übergang von einer erdölbasierten Wirtschaft in eine biobasierte Kreislauf-

wirtschaft. Filamentöse Pilze werden industriell normalerweise submers kultiviert, wobei ih-

re Morphologie stark mit der Produktivität korreliert. In vielen Anwendungen bilden sich

Hyphen-Agglomerate, sogenannte Pellets. Aufgrund ihrer Größe von bis zu einigen Millime-

tern und ihres dichten Hyphen-Netzwerks ist der Transport von Nährstoffen und Sauerstoff in

Pellets diffusionslimitiert, was sich auf die Produktivität auswirkt. Obwohl bekannt ist, dass

das Innere der Pellets ihre Produktivität beeinflusst, blieb es bisher weitgehend unerforscht.

Beispielsweise gibt es keine Methode, um das Hyphen-Netzwerk von ganzen Pellets zu analy-

sieren. Darüber hinaus fehlen Korrelationen zwischen der Pellet-Struktur und dem diffusiven

Stofftransport.

Im Zentrum dieser publikationsbasierten Dissertation befinden sich drei Paper, die zeigen,

wie die Morphologie und Diffusivität von filamentösen Pilz-Pellets bestimmt werden können.

Im ersten Paper wird basierend auf Röntgen-Mikrocomputertomographie (µCT) und dreidi-

mensionaler (3D) Bildanalyse die erste Methode zur Visualisierung und Analyse des Hyphen-

Netzwerks ganzer Pellets vorgestellt. Dadurch können einige morphologische Eigenschaften

einschließlich der Lage von Spitzen, Verzweigungen und Hyphen erstmals untersucht werden.

Das zweite Paper beschreibt den ersten Ansatz zur Korrelation der 3D-Struktur mit der Dif-

fusivität. Dafür wurden zahlreiche Diffusions-Berechnungen durch die Strukturen von Pel-

lets durchgeführt, welche aus µCT-Messungen gewonnen wurden. Im dritten Paper liefern

die Korrelationen zwischen den Diffusivitäten und Strukturen von 66 µCT gemessenen so-

wie 3125 Monte Carlo simulierten Pellets ein universelles Gesetz für die Diffusivität durch

filamentöse Netzwerke. Dabei decken die simulierten Pellets den breiten morphologischen

Bereich filamentöser Pilze ab. Unsere Daten zeigen, dass die Diffusivität einem einfachen

Skalierungsgesetz in Bezug auf den Feststoffvolumenanteil folgt.

Die Methoden und Erkenntnisse dieser Arbeit ermöglichen die Analyse der Mikromor-

phologie und die Vorhersage des diffusiven Stofftransports von Nährstoffen, Sauerstoff und

sekretierten Metaboliten in beliebigen filamentösen Pilz-Pellets. Diese Ergebnisse eröffnen

neue Möglichkeiten zum gezielten morphologischen Design von Pellets, um die Produktivi-

tät in der Pilzbiotechnologie zu erhöhen.

ii

Danksagung

Ein besonderer Dank geht an meinen Doktorvater Prof. Dr.-Ing. Heiko Briesen. Er hatte im-

mer ein offenes Ohr für meine Anliegen, war stets für neue Ideen zu begeistern und stellte eine

große Unterstützung dar. Außerdem bin ich Prof. Dr.-Ing. Andreas Kremling, Prof. Dr. Pe-

ter J. Punt und Prof. Dr.rer.nat. Philipp J. Benz sehr dankbar, dass Sie Teil der Prüfungskom-

mission sind.

Die aktuellen und ehemaligen Mitarbeiter am Lehrstuhl für Systemverfahrenstechnik er-

möglichten eine sehr gute Arbeitsatmosphäre. Vielen Dank! Dabei trugen vor allem Chri-

stoph, Michi, Hansi, Henri, Tiaan, Tijana, Thomas und Michaela durch fruchtbare Diskus-

sionen und ihre tatkräftige Unterstützung zu dieser Dissertation bei. Abseits der Arbeit am

Lehrstuhl möchte ich mich bei Hansi, Bernhard, Simon, Carsten, Christoph, Michi, Lakshmi,

Lars und Henri für viel Spaß und Freude bedanken! Vielen Dank an Tiaan Friedrich, Hen-

ri Müller, Christian Preischl, Johannes Zuber, Lorenz Thurin, Miriam Stoll, Nadine Münch,

Andreas Laible, Markus Betz, Pamina Füting, Regina Forstner, Sophia Bonzel, Simon Wa-

gensoner, The Anh Baran und Clarissa Schulze. Eure Betreuung und unsere Zusammenarbeit

hat mir immer Spaß gemacht und häufig meinen Horizont erweitert.

Ein sehr großer Dank geht an Lars, Marcel, Kathrin, Ludwig, Vera und Rainer Krull. Ihr

habt mir die interessante Welt der filamentösen Mikroorganismen gezeigt und dabei viel Ge-

duld mit mir gehabt! Für das Korrekturlesen dieser Arbeit und viele hilfreiche Hinweise danke

ich Lars, Henri, Christoph, Caro und meinem Bruder Andi.

Am Meisten möchte ich mich bei meinen Eltern, Caro, meinem Bruder Andi und allen

Freunden von ganzem Herzen für ihre Unterstützung, Geduld, Freundschaft und Hilfsbereit-

schaft bedanken. Insbesondere meine Eltern ermöglichten mir mein Studium und damit auch

diese Promotion. Danke!

iii

Contents

1 Introduction 1

2 Theoretical background 3

2.1 Morphology of pellets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Morphological development: from spore to pellet . . . . . . . . . . . 3

2.1.2 Morphological properties . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.3 Applicability of morphological measurement techniques . . . . . . . 8

2.2 Interplay between morphology, transport of nutrients, and metabolic activity

of pellets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Spatial distribution and mass transport of nutrients inside pellets . . . 10

2.2.2 Metabolic activity . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Morphological engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.1 Experimental approaches . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.2 Modeling approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Problem definition 19

4 Methods for problem solving 20

5 Results 21

5.1 An X-ray microtomography-based method for detailed analysis of the three-

dimensional morphology of fungal pellets . . . . . . . . . . . . . . . . . . . 21

5.2 From three-dimensional morphology to effective diffusivity in filamentous

fungal pellets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.3 Universal law for diffusive mass transport through mycelial networks . . . . . 49

6 Discussion 75

6.1 Morphological analysis of pellets . . . . . . . . . . . . . . . . . . . . . . . . 75

6.2 Diffusive transport through mycelial networks . . . . . . . . . . . . . . . . . 77

6.3 New paths towards morphological engineering . . . . . . . . . . . . . . . . . 79

7 References 83

8 Appendix: List of Publications 91

v

1 Introduction

In 1917, the food chemist James Currie described the filamentous fungus Aspergillus niger as

an efficient producer of citric acid. Only two years later, mass production of citric acid started

and industrial biotechnology was born (Cairns et al., 2018). Further, the discovery of peni-

cillin as a filamentous fungal metabolite in Penicillium chrysogenum (Fleming, 1929) and the

industrialization thereof during World War II was probably the most important breakthrough

of fungal biotechnology and started the antibiotic era. Today, filamentous fungi are still in-

dispensable for the mass production of citric acid (Cairns et al., 2018; Meyer et al., 2020)

and antibiotics (Keller, 2019; Zacchetti et al., 2018), opening multibillion dollar markets and

being a lifesaver for millions of people (Demain, 2014). While large-scale manufacturing

processes have been developed for several products (Meyer et al., 2016), filamentous fungal

biotechnology has emerged as a hope for a sustainable future (Meyer et al., 2020). According

to a thinktank consisting of researchers and companies, filamentous fungal biotechnology can

be key for the transition from a petroleum-based economy into a bio-based circular economy

(Meyer et al., 2020). Thus, this biotech sector will make significant contributions to climate

change mitigation and will meet several United Nations’s sustainable development goals.

Filamentous fungi are favorable hosts for many biotechnological applications (Wösten,

2019) including the production of acids, enzymes, and secondary metabolites (Hoffmeister

and Keller, 2007; Meyer, 2008; Punt et al., 2002). Compared to bacteria, filamentous fungi

benefit from their ability to perform complex post-translational modifications (Wang et al.,

2020), their greatly expanded protein secretion apparatus (Ward, 2012), and their potential

to produce various bioactive molecules (Brakhage, 2013; Keller, 2019; Nielsen et al., 2017).

Further, filamentous fungi are the only microorganisms with the ability to fully degrade lig-

nocellulosic biomass sustainably to a rich and diverse set of useful products (Meyer et al.,

2020).

In industrial biotechnology, filamentous fungi are usually cultivated under submerged con-

ditions. In such processes, fungal morphology affects productivity (Böl et al., 2021; Krull

et al., 2013; Veiter et al., 2018). Generally, filamentous fungi consist of branched tubes called

hyphae and the macromorphology ranges from loose dispersed hyphae to dense hyphal ag-

glomerates called pellets (Papagianni, 2004; Veiter et al., 2018). Both macromorphologies,

dispersed hyphae and pellets, come with some advantages and limitations. Dispersed hyphae

result in a high viscosity of the cultivation broth, and thus, reduce the nutrient supply due to

insufficient mixing (Krull et al., 2010, 2013). Contrary, cultivation broths with pellets as pre-

dominant macromorphology show low viscosities (Cairns et al., 2019b; Krull et al., 2013).

Compared to dispersed hyphae, pellets display enhanced resistance to shear stress (Cairns

et al., 2019b). However, the transport of nutrients and oxygen into pellets is diffusion-limited

1

by the dense structure (Hille et al., 2005, 2009), which alters growth, metabolic activity, and

finally product formation (Cairns et al., 2019b; Krull et al., 2013; Veiter et al., 2018).

The inner structure of pellets, e.g., the spatial distribution of tips and hyphal material,

is known to affect their productivity. However, the micromorphology within whole intact

pellets has not yet been determined. Similarly, there are no correlations between the three-

dimensional (3D) structure and the diffusive mass transport of nutrients, oxygen, and secreted

metabolites within pellets. Both knowledge gaps are caused by the absence of techniques to

measure and analyze the microscopic structure of whole pellets.

In this publication-based dissertation, methods based on X-ray microcomputed tomogra-

phy (µCT) measurements and 3D image analysis were developed to determine the micro-

morphology of whole pellets (Paper I). Further, a method for diffusion computations through

3D images of pellets was developed (Paper II). As counterpart to the measured pellets, a

3D Monte Carlo growth approach was extended to enable the formation of pellets with the

broad morphological range of filamentous microorganisms (Paper III). Diffusion computa-

tions through 66 measured pellets originating from four filamentous fungi and 3125 simu-

lated pellets revealed a universal correlation between the structure and diffusivity of hyphal

networks (Paper III).

Based on the described methods and findings, micromorphologies of whole intact pellets

can be determined and the diffusion of nutrients, oxygen, and secreted metabolites through

dense hyphal networks can be predicted. Applying 3D morphological analysis of pellets,

the outcome of morphological engineering approaches can be investigated in utmost detail.

In addition, existing approaches to model the morphological development of pellets can be

validated and improved through the use of 3D morphological data and the universal diffu-

sion law. Thus, this thesis will contribute to the targeted design of pellet morphologies, i.e.,

morphological engineering, and to enhanced productivities in fungal biotechnology.

2

2 Theoretical background

Cultivated under submerged conditions, the macromorphology of filamentous fungi ranges

from dispersed hyphae to dense hyphal agglomerates called pellets (Krull et al., 2013; Veiter

et al., 2018). Due to limitations in characterizing the structure and mass transport processes

inside pellets, the focus of this dissertation is on pelletized fungi. Because filamentous bacte-

ria and filamentous fungi in sumberged cultures are similar from a morphological perspective

(Böl et al., 2021; Olmos et al., 2013; Zacchetti et al., 2018), the methods to characterize

and model their morphology are often identical. Furthermore, the mass transport of nutrients

and oxygen through both fungal and bacterial pellets is limited by the dense hyphal network

and the inner part of pellets can be starved (Böl et al., 2021; Zacchetti et al., 2018). Due to

these similarities between filamentous fungi and filamentous bacteria, a selection of findings

and methods for filamentous bacteria are also mentioned in this dissertation. In Section 2.1,

the morphology is elaborated. The interplay between morphology and metabolic activity

and resulting morphological engineering approaches for pellets are described in Sections 2.2

and 2.3, respectively.

2.1 Morphology of pellets

This section describes the development of pellets in submerged cultures, morphological prop-

erties, and morphological measurement techniques.

2.1.1 Morphological development: from spore to pellet

Spores play a crucial role for the formation of pellets (Krull et al., 2013; Zhang and Zhang,

2016). Thus, the development of pellets starting from spores is described here.

Filamentous fungal spores are produced under stressful environmental conditions to ensure

the survival of the organism and can be assumed as metabolically inactive cells (Riquelme

et al., 2018). When bioprocesses are inoculated with spores, favorable conditions activate

their metabolism, initiate swelling, and ultimately, result in germ tube formation (Bizukojc

and Ledakowicz, 2006; Paul et al., 1993). Germ tubes represent first hyphal elements and

grow, like all fungal hyphae, based on tip extension. Both germination and the growth of

hyphae are polarized processes, i.e., the formation of new cell composites is directed. Thus,

tubular structures are created (Cairns et al., 2019b; Riquelme et al., 2018). The simultaneous

extension of tips and the development of new tips by branching of hyphae result in filamen-

tous networks. This process leads to an exponential increase of the biomass under unlimited

growth conditions (Krull et al., 2010).

3

Traditionally, it is distinguished between coagulative and non-coagulative pellet formation

types (Metz and Kossen, 1977), which are illustrated in Figure 1. During non-coagulative

pellet formation, spores and germinated spores remain dispersed. For example, Žnidaršic

et al. (1998) showed that Rhizipus stolonifer (synonym R. nigricans) pellets can develop from

single spores. Contrary, coagulative pellets can form from hundreds or thousands of agglom-

erated spores (Fontaine et al., 2010; Metz and Kossen, 1977). A classical representative of

the coagulative type is Aspergillus niger (Cairns et al., 2018). However, different cultivation

conditions cause different morphological behaviors and a final classification of an organism

into coagulative or non-coagulative type is difficult (Veiter et al., 2018; Zhang and Zhang,

2016). For instance, Nielsen et al. (1995) showed that Penicillium chrysogenum exhibit char-

acteristics of both types. In their study, spores remained dispersed whereas branched hy-

phae agglomerated and subsequently developed to pellets. Thus, Veiter et al. (2018) assigned

P. chrysogenum to a third group, the hyphal element agglomerating type.

Figure 1: Development of non-coagulative and coagulative pellets. Spores are marked black,whereas hyphae are grey. Three-dimensional morphologies were simulated with an ownstochastic growth-model that is based on Celler et al. (2012). Scale bar: 100 µm.

2.1.2 Morphological properties

According to Krull et al. (2013), “pellets can be described as stable spherical agglomerates

composed of a branched network of hyphae. Their shape can vary from smooth and spheri-

cal to elongated and hairy” (p. 113). Further, the micromorphology describes the details of

the hyphal network (Krull et al., 2013; Veiter et al., 2018). In this subsection, quantitative

morphological properties of filamentous microorganisms are described together with their

measurement techniques. The advantages and limitations of the mentioned techniques are

elaborated in Section 2.1.3. To group morphological properties of pellets, they are assigned

to the following classes: size, shape, compactness, morphology number, and spatial distri-

bution of hyphal material. In addition, micromorphological descriptors for dispersed hyphae

4

exist. However, due to a lack of suitable methods, these descriptors have not yet been studied

for pellets. Table 1 gives an overview of morphological properties and their corresponding

measurement techniques, which are elaborated in the following.

Size The size of individual pellets is specified by the projected area, various diameters,

perimeter, chord length, and signal length. Additionally, size distributions of pellet popula-

tions can be investigated.

The projected area is the two-dimensional area of the projection of a three-dimensional

object on a plane and often applied to pellets (Cairns et al., 2019a; Walisko et al., 2017;

Wucherpfennig et al., 2011). To determine the projected area, two-dimensional images are

acquired and analyzed. Based on the projected area, different diameters can be calculated.

The Feret diameter is defined as the distance between two parallel lines touching the edge of

the projected area (Cairns et al., 2019a; Walisko et al., 2017; Wucherpfennig et al., 2011). Ad-

ditionally, the surface equivalent spherical diameter of the projected area can be determined

(Schrinner et al., 2020). Some studies investigated the perimeter, defined as the total length of

the object boundary. A distinction is made between the perimeter of the convex area (Cairns

et al., 2019a; Wucherpfennig et al., 2011) and the perimeter of the projected area (Schrinner

et al., 2020; Walisko et al., 2017).

With focused beam reflectance measurement (FBRM) (Grimm et al., 2004; Kelly et al.,

2006; Lin et al., 2008; Pearson et al., 2003, 2004) and novel flow cytometry systems (Ehgart-

ner et al., 2017; Schrinner et al., 2020; Veiter and Herwig, 2019), the chord length and signal

length of pellets can be investigated, respectively. While the previously mentioned techniques

enable the investigation of numerous pellets individually, the application of laser diffraction

ultimately results in a size distribution of pellets (Lin et al., 2010; Petersen et al., 2008; Quin-

tanilla et al., 2018; Rønnest et al., 2012; Wucherpfennig et al., 2011).

Shape Based on image analyses of the projected area, the shape parameters circularity and

aspect ratio can be investigated. Schrinner et al. (2020) and Wucherpfennig et al. (2011)

applied the circularity, which is a function of the projected area and the perimeter:

Circularity = 4πPro jected area

Perimeter2 . (2.1)

While the projection of a perfect sphere would have a circularity of 1, values closer to 0

indicate elongated and/or non-convex objects. The aspect ratio is defined as the ratio between

the maximum and minimum Feret diameter (Cairns et al., 2019a; Wucherpfennig et al., 2011).

Symmetrical objects in all axis such as circles or squares would have an aspect ratio of 1,

whereas elongated objects result in higher aspect ratios. Thus, the aspect ratio is applied to

describe the elongation of pellets (Cairns et al., 2019a; Wucherpfennig et al., 2011).

Compactness The solidity is described as a surface property, measured on base of image

analysis, and defined as the ratio between the projected area and the convex area (Cairns

et al., 2019a; Wucherpfennig et al., 2011). A convex shape would result in a solidity of 1,

5

Table1:M

orphologicalpropertiesdeterm

inedforpellets

anddispersed

hyphaeC

lassProperty

TechniqueR

eferences

PelletSize

Projectedarea

Microscopy

Barry

etal.(2015);Cairns

etal.(2019a);Schrinneretal.(2020);Walisko

etal.(2017);W

ucherpfennigetal.(2011)

Diam

eterM

icroscopyC

airnsetal.(2019a);Schrinner

etal.(2020);Walisko

etal.(2017);Willem

seetal.(2018);W

ucherpfennigetal.(2011)

Perimeter

Microscopy

Cairns

etal.

(2019a);Schrinner

etal.

(2020);W

aliskoet

al.(2017);

Wucherpfennig

etal.(2011)C

hordlength

FBR

MG

rimm

etal.(2004);Kelly

etal.(2006);Pearsonetal.(2003,2004)

SignallengthFlow

cytometry

Ehgartneretal.(2017);Schrinneretal.(2020);V

eiterandH

erwig

(2019)Size

distributionL

aserdiffrac-

tionL

inetal.(2010);Petersen

etal.(2008);Quintanilla

etal.(2018);Rønnestetal.

(2012);Wucherpfennig

etal.(2011)Shape

Circularity

Microscopy

Barry

etal.(2015);Schrinneretal.(2020);Walisko

etal.(2017);Wucherpfen-

nigetal.(2011)

Aspectratio

Microscopy

Cairns

etal.(2019a);Wucherpfennig

etal.(2011)C

ompactness

Solidityofperiphery

Microscopy

Cairns

etal.(2019a);Wucherpfennig

etal.(2011)R

elativeannulardiam

-eter

Flowcytom

etryE

hgartneretal.(2017)

Com

pactnessofcore

Flowcytom

etryE

hgartneretal.(2017);Schrinneretal.(2020);Veiterand

Herw

ig(2019)

Com

binationof

size,shape,

andcom

pact-ness

Morphology

number

Microscopy

Cairns

etal.(2019a);Wucherpfennig

etal.(2011)

Spatialdistribution

ofhyphalm

aterialH

yphalfractionM

icroscopyof

slicesH

illeetal.(2005,2009)

Dispersed hyphae

Microm

orphologyof

dispersedhyphae

TotalhyphallengthM

icroscopyB

arryetal.(2015);B

ockingetal.(1999);C

ardinietal.(2020);Kw

onetal.

(2013);L

ecaultet

al.(2007);Sachs

etal.(2019);

Schmideder

etal.(2018);

Vidal-D

iezde

Ulzurrun

etal.(2019)N

umberoftips

Microscopy

Barry

etal.(2015);Lecaultetal.(2007);Sachs

etal.(2019);Schmidederetal.

(2018);Vidal-D

iezde

Ulzurrun

etal.(2019)N

umberofbranches

Microscopy

Barry

etal.(2015);Lecaultetal.(2007);Sachs

etal.(2019);Schmidederetal.

(2018)H

yphalgrowth

unitM

icroscopyB

arryet

al.(2015);

Bocking

etal.

(1999);C

hoyet

al.(2011);

Colin

etal.

(2013);Kw

onetal.(2013);Sachs

etal.(2019)B

ranchangle

Microscopy

Du

etal.(2016);Lehm

annetal.(2019);Y

angetal.(1992b)

InternodallengthM

icroscopyD

uetal.(2016);L

ehmann

etal.(2019);Sachsetal.(2019)

Hyphaldiam

eterM

icroscopyC

hoyetal.(2011);C

olinetal.(2013);L

ehmann

etal.(2019)

6

whereas non-convex shapes would result in lower values. Based on forward scatter signals

of flow cytometry, the properties relative annular diameter (RAD) and compactness can be

determined (Ehgartner et al., 2017). RAD describes the ratio of the loose pellet periphery to

the whole pellet whereas compactness represents the uniformity of the density of the pellet

core.

Combination of size, shape, and compactness Based on a combination of several

properties determined from image analysis, the dimensionless morphology number can be

investigated (Wucherpfennig et al., 2011):

morphology number =2√

A S√π D E

, (2.2)

where A is the projected area, S the solidity, D the maximum Feret diameter, and E the

elongation (aspect ratio). Perfectly round and convex pellets would result in a morphology

number of 1, whereas elongated and/or non-convex pellets would result in lower morphology

numbers.

Spatial distribution of hyphal material An established method to visualize the interior

of pellets is to acquire images of slices. In brief, pellets are frozen in embedding medium

and then cut into slices with a thickness of about 50 - 100 µm. Images of the slices are taken

either with light (Lin et al., 2010; Priegnitz et al., 2012) or confocal laser scanning (Hille

et al., 2005, 2009) microscopy. Lin et al. (2010) and Priegnitz et al. (2012) described the

spatial distribution of hyphal material only qualitatively by the appearance of dense and loose

regions in the pellet. Contrary, Hille et al. (2005, 2009) applied quantitative descriptors. They

investigated the hyphal fraction, i.e., the ratio of the volume of hyphae to the total volume, as

a function of the pellet radius.

Micromorphology of dispersed hyphae Because hyphae of more complex structures

superimpose, 2D image analysis can be only applied to investigate the micromorphology of

mycelia with a few branches. One important property is the total hyphal length, which can

be investigated manually with the help of measurement tools implemented in image analysis

softwares (Bocking et al., 1999; Kwon et al., 2013). Additionally, it can be determined auto-

matically by the investigation of the mycelial skeleton (Figure 2), which is the centerline of

hyphae with a thickness of one pixel (Barry et al., 2015; Cardini et al., 2020; Lecault et al.,

2007; Sachs et al., 2019; Schmideder et al., 2018; Vidal-Diez de Ulzurrun et al., 2019). Each

pixel of the skeleton can be assigned to be a tip (one neighbor), hyphae (two neighbors), or

branch (three neighbors). Four neighboring pixels would be assigned to the junction of two

overlapping hyphae. As shown in Figure 2, the number of tips and number of branches can

be investigated automatically based on analyses of the skeleton (Barry et al., 2015; Lecault

et al., 2007; Sachs et al., 2019; Vidal-Diez de Ulzurrun et al., 2019). However, the number of

tips and number of branches are often counted manually (Bocking et al., 1999; Kwon et al.,

2013). Dividing the total hyphal length by the number of tips results in the hyphal growth unit

7

(HGU) (Barry et al., 2015; Bocking et al., 1999; Choy et al., 2011; Colin et al., 2013; Kwon

et al., 2013; Sachs et al., 2019). Similar to the HGU, the internodal length (distance between

two branches) can be determined as a measure for the branching frequency (Du et al., 2016;

Lehmann et al., 2019; Sachs et al., 2019). Further, the hyphal diameter (Choy et al., 2011;

Colin et al., 2013; Lehmann et al., 2019) and the branch angle (Du et al., 2016; Lehmann

et al., 2019; Yang et al., 1992b) can be investigated.

Figure 2: Analysis of morphological development of Aspergillus niger mycelia: black marksthe centerlines of hypha, green the tips, and blue the branches. A1 - A4) Development ofmycelium A. B1 - B4) Development of mycelium B. In A5 and B5, the analyzed centerlinesof A4 and B4 are illustrated along with their respective microscopic image. Image analysisprocedure was adapted from Schmideder et al. (2018).

2.1.3 Applicability of morphological measurement techniques

Usually, microscopy is applied to determine the morphology of pellets. While, FBRM, laser

diffraction, and flow cytometry have become fast alternatives to microscopy, they often lead

to less detailed information. In the following, the advantages and limitations of the mentioned

measurement techniques are elaborated.

Light microscopy The state of the art to characterize the morphology is light microscopy

(Papagianni, 2014). Today, several open source image analysis tools simplify the offline-

analysis of pellets (Barry et al., 2015; Willemse et al., 2018) and dispersed hyphae (Barry

et al., 2015; Brunk et al., 2018; Cardini et al., 2020; Sachs et al., 2019; Vidal-Diez de Ulzurrun

et al., 2019). Further, the germination of spores (Brunk et al., 2018) and the tip extension and

branch formation of dispersed hyphae (Schmideder et al., 2018) can be tracked time-resolved

when the spores are fixed in a growth chamber (Figure 2). A combination of these tools,

the ubiquitous presence of light microscopes in laboratories, the opportunity to study diverse

morphological properties (compare Table 1), and the possibility to investigate hundreds of

pellets per time point (Schrinner et al., 2020) will further drive the use of light microscopy

to study filamentous microorganisms. However, the superimposition of hyphae hinders the

straightforward analysis of the micromorphology of more complex structures such as pellets.

8

Confocal laser scanning microscopy Contrary to 2D light microscopy, CLSM enables

to visualize the 3D morphology. However, CLSM requires a fluorescent signal and is limited

to about 50 - 150 µm in penetration depth. Thus, only the periphery can be visualized without

cutting the pellets (Hille et al., 2005, 2009; Villena et al., 2010). For unknown reasons, exist-

ing studies lack subsequent image analysis to investigate the micromorphology of the pellet

periphery. To determine the spatial distribution of the hyphal fraction inside pellets, Hille

et al. (2005, 2009) analyzed CLSM measurements of slices. However, the determined hyphal

fraction did not reflect the reality, since they used overlays of the acquired z-stacks. Thus, the

hyphal fraction was often 100 %, which is impossible even for densest packing. To the au-

thor’s knowledge there is no approach that analyzes the three-dimensional micromorphology

based on CLSM measurements.

Focused beam reflectance measurement FBRM enables the analysis of the chord

length and concentration of spores, spore agglomerates, and pellets offline (Pearson et al.,

2003, 2004; Whelan et al., 2012) as well as inline (Grimm et al., 2004; Kelly et al., 2006; Lin

et al., 2008). Advantages of FBRM are the inline applicability and the potential to measure

large quantities of objects. However, information about the shape and periphery of pellets are

missing and data interpretation remains challenging.

Laser diffraction To investigate the size distribution of spore agglomerates and pellets,

laser diffraction can be applied (Lin et al., 2010; Petersen et al., 2008; Quintanilla et al., 2018;

Rønnest et al., 2012; Wucherpfennig et al., 2011). Based on Fraunhofer diffraction theory,

the diffraction pattern of a laser beam can be analyzed to calculate the volumetric pellet size

distribution that best matches the measured pattern (Lin et al., 2010). Wucherpfennig et al.

(2011) applied laser diffraction in a bypass, whereas the other authors took samples before the

measurements. Laser diffraction has the advantage to be much faster than more commonly

used microscopy (Lin et al., 2010; Petersen et al., 2008; Quintanilla et al., 2018; Rønnest

et al., 2012). However, it fails to report properties that describe the shape and periphery of

pellets (Petersen et al., 2008; Wucherpfennig et al., 2011) as well as the pellet concentration

(Lin et al., 2010). According to Rønnest et al. (2012), the analysis is based on a number of

assumptions. For example, the shape of filamentous structures has to be assumed. However,

the authors suggested that validation studies could contribute to a reliable technique to analyze

size distributions of filamentous microorganisms.

Flow cytometry Ehgartner et al. (2017) described flow cytometry as a fast alternative to

microscopy. Further, they envision an online application through automated sampling sys-

tems. Similar to image analysis, flow cytometry allows the quantification of the pellet size

and the identification of the hairy region of the pellet periphery (Ehgartner et al., 2017; Schrin-

ner et al., 2020; Veiter and Herwig, 2019). In addition, flow cytometry reveals a compactness

parameter of pellets. However, information about the projected area is lacking and size ex-

clusion of samples occurs, which can result in an over-representation of small pellets (Veiter

and Herwig, 2019).

9

2.2 Interplay between morphology, transport of nutrients, and

metabolic activity of pellets

The interplay between morphology, transport of nutrients, and metabolic activity is a key

aspect for the productivity of filamentous pellets (Papagianni, 2004; Veiter et al., 2018; Zac-

chetti et al., 2018). In general, the optimal morphology varies with the desired product and

cannot be generalized (Gibbs et al., 2000; Krull et al., 2010). For example, the pellet form of

Aspergillus niger is used to produce citric acid, whereas its dispersed form serves for the pro-

duction of enzymes (Meyer et al., 2016). While pellets have some advantages over dispersed

hyphae (Section 1), limited nutrient availability (Cairns et al., 2019b; Krull et al., 2013) might

occur within pellets. For example, the concentration of oxygen is known to decrease towards

the center of pellets (Hille et al., 2005, 2009). This leads to a reduced growth and metabolic

activity in the core (Cairns et al., 2019b; Veiter et al., 2018) and can limit the production of

enzymes (Driouch et al., 2010; Veiter et al., 2018). However, reduced metabolic activity in

the center of pellets can also increase the production of secondary metabolites (Cairns et al.,

2019b; Veiter et al., 2018) such as Penicillin (Cronenberg et al., 1994). This demonstrates

that a detailed understanding of the profile of nutrients and the resulting metabolic activity in

pellets is of crucial importance.

2.2.1 Spatial distribution and mass transport of nutrients inside pellets

The spatial distribution of nutrients inside pellets is determined by metabolic rates and trans-

port processes through their dense structure (Celler et al., 2012; Cui et al., 1998). In the

following section, the focus is on the investigation of nutrient profiles in pellets and mass

transport properties of hyphal networks.

Profile of nutrients In general, studies measuring the profile of nutrients are rare. A rea-

son might be the need of complicated experimental setups, where pellets are fixed in defined

chambers before the concentration profile of oxygen or glucose can be measured with micro-

electrodes (Cronenberg et al., 1994; Hille et al., 2005, 2009; Wittier et al., 1986). To guarantee

a realistic nutrient transport and keep the morphology intact, the handling of the pellets and

microelectrodes as well as the design and control of the chambers are challenging. For exam-

ple, Hille et al. (2005, 2009) applied a thin microelectrode with a tip diameter similar to the

diameter of hyphae.

Experiments unveiled oxygen as prime limiting nutrient in fungal pellets (Cronenberg et al.,

1994; Veiter et al., 2018). Measurements of the oxygen profile in pellets greater than 1 mm

revealed a restricted availability of oxygen with only the outer 100 - 300 µm being supplied

(Cronenberg et al., 1994; Hille et al., 2005, 2009; Wittier et al., 1986). In addition to oxygen,

Cronenberg et al. (1994) determined the concentration profile of glucose. Although glucose

penetrated Penicillium chrysogenum pellets at early cultivation stages almost at bulk level, no

glucose consumption was determined in their core. Since fungal metabolism requires oxygen,

this was explained by the measured absence of oxygen in the core. At late cultivation stages,

10

the pellets were prone to fragmentation and autolysis and showed a decreased metabolic ac-

tivity in the core. While pellets were completely penetrated by oxygen and glucose, glucose

consumption still only occurred in the periphery. The authors explained the lost metabolic ac-

tivity in the core by the irreversible inhibition in early cultivation stages caused by the absence

of oxygen.

Especially Cronenberg et al. (1994) demonstrated the interplay between the profile of nu-

trients and the metabolic activity in pellets. Further, all mentioned studies revealed that con-

centration profiles in pellets are highly affected by their structure. In addition to the size of

pellets, the density plays a decisive role. For example, Hille et al. (2005) observed a much

steeper decrease of the oxygen concentration in dense A. niger pellets. Moreover, measuring

the development of nutrient profiles in inactivated pellets is the only method to investigate

their diffusivity, which is be elaborated in the following.

Mass transport of nutrients Many authors suggest diffusion as the only mass transport

phenomenon of oxygen and nutrients inside pellets (Cui et al., 1998; King, 1998; Silva et al.,

2001). In addition to diffusive transport, convective transport is proposed to contribute to the

nutrient-supply of pellets with a loose periphery, especially if they are prone to turbulent flow

regimes (Cronenberg et al., 1994; Hille et al., 2009). Because diffusive mass transport was

shown to be the most important transport phenomenon inside pellets, its theoretical back-

ground is elaborated in the following. The diffusivity of component i is described with the

effective diffusion coefficient Di,eff (Becker et al., 2011):

Di,eff = Di,bulk · keff , (2.3)

where Di,bulk is the diffusion coefficient in the pure bulk medium and keff determines the

reduction to the effective diffusion coefficient. While the effective diffusion factor keff is

dependent on the geometry of the pores, it is independent of the diffusing substance.

Besides measurement of nutrient profiles, Cronenberg et al. (1994) and Hille et al. (2009)

investigated the effective diffusivity of P. chrysogenum and A. niger pellets, respectively. For

this purpose, Hille et al. (2009) placed one microelectrode each at the periphery and in a de-

fined depth of inactivated pellets. The inactivation of the pellets prevented the consumption

of oxygen. After saturating the medium with nitrogen, the measurement chamber was aerated

with pure oxygen and the change of the concentration was recorded by both microelectrodes.

Based on the development of the concentrations and Fick’s second law, they were able to

fit the effective diffusion coefficient. Similar to Hille et al. (2009), Cronenberg et al. (1994)

determined the development of the oxygen or glucose concentration by stimulus response ex-

periments inside inactivated pellets to further estimate the effective diffusivity. As expected,

dense pellet peripheries resulted in low effective diffusivities. The minimum effective diffu-

sion factor ke f f was about 0.4 and 0.6 in the studies of Hille et al. (2009) and Cronenberg

et al. (1994), respectively. As Cronenberg et al. (1994) described the morphology of pellet

slices only qualitatively, they were not able to correlate the morphology with the effective

diffusivity. Contrary, Hille et al. (2009) quantified the morphology of pellet slices with the

11

radial profile of the hyphal fraction. However, as mentioned in Section 2.1.3, they missed the

three-dimensional information of the hyphal network. Thus, hyphae superimposed in two-

dimensional projections of slices and the hyphal fraction was often 100 %. That is impossible

even for densest packing. Nevertheless, they correlated the effective diffusivity with the local

derivation of the hyphal fraction.

To the author’s knowledge, Hille et al. (2009) was the only experimental approach to

correlate the morphology and diffusivity of hyphal networks. Although studies about fi-

brous materials revealed that porosity and tortuosity are important drivers of ke f f (Tomadakis

and Robertson, 2005; Vignoles et al., 2007), modeling approaches of filamentous pellets

(Buschulte, 1992; Cui et al., 1998; Lejeune and Baron, 1997; Meyerhoff et al., 1995) ei-

ther neglect the tortuosity of the hyphal network or assume a constant value to model the

diffusivity of nutrients. A detailed list of applied and determined correlations between the

morphology and effective diffusion factors of filamentous microorganisms and fibrous mate-

rials can be found in Paper II, Table 1.

2.2.2 Metabolic activity

The limited availability of nutrients in central parts of pellets can lead to a physiological

heterogeneity inside pellets (Zacchetti et al., 2018) and to a reduced growth and growth-

related metabolism (Hille et al., 2009; Zhang and Zhang, 2016). Metabolic activity can be

identified by staining and analyzing active as well as inactive regions. In this way, many

studies determined metabolic inactive cores and active shell layers of pellets. Staining as

indicator of metabolic activity is conducted either with chemicals (Bizukojc and Ledakowicz,

2010; Nieminen et al., 2013; Schrinner et al., 2020; Veiter and Herwig, 2019) or by using

fluorescence proteins expressed by the host organism (Driouch et al., 2012, 2010; Tegelaar

et al., 2020).

The author of this dissertation contributed to a cooperative study about the metabolic ac-

tivity in filamentous bacterial pellets (Schrinner et al., 2020), which is not embedded in the

results section of this thesis. In this study, active and inactive regions of Lentzea aerocoloni-

genes pellets were stained with SYTO9 (green fluorescence through intercalation with DNA

of predominantly intact and active cells) and propidium iodide (red fluorescence as result from

DNA intercalation in inactive cells with compromised membranes), respectively. As illus-

trated in Figure 3, metabolically different regions of pellet slices were distinguished through

the analysis of CLSM images. Because pellet slicing followed by image analysis is of high

manual effort, flow cytometry was applied to detect active and inactive fractions of hundreds

of stained pellets. While flow cytometry enabled the analysis of a statistically relevant number

of pellets, image analysis of pellet slices provided shape information.

Fluorescence staining of active and inactive pellet regions can also be applied to filamen-

tous fungi. Similar to the mentioned study about filamentous bacteria (Schrinner et al., 2020),

Veiter and Herwig (2019) analyzed P. chrysogenum pellets based on CLSM and flow cytom-

etry. Bizukojc and Ledakowicz (2010) stained growing regions of Aspergillus terreus with

lactophenol methyl blue. This staining procedure allows to analyze growing regions through

12

Figure 3: Determination of living (green), dead (red) and a combination of living and dead(yellow) pellet areas. Image analysis was performed based on CLSM measurements of stainedLentzea aerocolonigenes pellet slices. (a) Original image with green and red fluorescent areas(black circles are air bubbles that are occasionally enclosed in the sectioning medium). (b)Separation in green fluorescence and red fluorescence. (c) Processed images. (d) Imagewith living, dead, and a combination of living and dead pellet areas. Figure is from jointpublication (Schrinner et al., 2020).

light microscopy of pellet slices. Further, the authors correlated the fraction of active growing

regions with the formation of the desired product lovastatin. Instead of activity staining with

chemicals, Driouch et al. (2012, 2010) engineered genetically modified A. niger strains that

co-express green fluorescent protein (GFP) together with the desired product glucoamylase

or fructofuranosidase, respectively. Thus, they were able to quantify metabolic active regions

based on CLSM images of pellet slices. In Driouch et al. (2012), large pellets were only

active in a 200 µm surface layer. The authors concluded that the inner region of large pellets

does not contribute to the production of the desired enzymes, which is probably caused by

diffusion limitation of oxygen or other nutrients.

In several studies, the volume fraction of the active shell layer and the formation of desired

products increased with decreasing pellet diameter (Bizukojc and Ledakowicz, 2010; Dri-

ouch et al., 2012, 2010; Tegelaar et al., 2020). However, a correlation between the metabolic

activity and the detailed morphology within pellets, e.g., the spatial distribution of hyphal

material and the number of (active) tips, is lacking. Additionally, there is no study to date that

determines both the nutrient profile and metabolic heterogeneity within pellets.

13

2.3 Morphological engineering

There is no doubt that the morphology of filamentous microorganisms strongly affects their

productivity in submerged cultures. Thus, the precise control of the morphology, i.e., morpho-

logical engineering, is of crucial importance (Krull et al., 2013). In this Section, experimental

and modeling approaches are described to engineer the morphology of filamentous pellets.

2.3.1 Experimental approaches

In this thesis, it is distinguished between genetic and process engineering approaches to alter

the morphology.

Genetics Two recent reviews highlight genetic aspects that impact the morphogenesis of

filamentous fungi (Cairns et al., 2019b; Zhang and Zhang, 2016). In the following, a few

exemplary filamentous fungal characteristics are described that can be specifically modified

to allow targeted strain development.

As stated earlier, spore agglomeration is one of the driving factors for the formation of pel-

lets. One known factor for spore agglomeration is their hydrophobicity (Zhang and Zhang,

2016). The absence of spore cell wall associated hydrophobins DewA and RodA in As-

pergillus nidulans knockout mutants reduced the ratio of biomass present as pellets. Further,

the average size of pellets decreased (Dynesen and Nielsen, 2003). Fontaine et al. (2010)

showed that cell wall 1-3glucans become exposed at the cell surface during spore swelling and

induce the agglomeration of germinating Aspergillus fumigatus conidia. Additionally, spores

of species with 1-3glucan synthase gene (ags) in their genome (A. fumigatus and P. chryso-

genum) agglomerate, whereas no spore agglomeration can be observed for organisms without

ags (R. oryzae and Trichoderma reesii). Further, A. niger alb1 knockout mutants are deficient

in melanin biosynthesis and showed altered surface structures and charge of spores (Priegnitz

et al., 2012). The authors concluded that spore agglomeration differs between the wild type

and the mutant in pH-dependent manner due to the changed surface charge.

Besides spore agglomeration, the branching frequency has a strong influence on the mor-

phological development (Cairns et al., 2019b). As shown by several authors, the branching

frequency can be genetically modified (Biesebeke et al., 2005; Fiedler et al., 2018; He et al.,

2016; Kwon et al., 2013). Fiedler et al. (2018) reported more compact macromorphologies

of the hyperbranching phenotype. In addition to the change in morphology, productivity can

also be altered by the branching frequency. Especially for the production of enzymes, a high

tip to biomass ratio seems to be beneficial (Biesebeke et al., 2005; He et al., 2016). However,

in some cases an elevated tip to biomass ratio cannot be correlated with an increased protein

titer (Cairns et al., 2019b).

The described genetic modifications prove that the morphology can be influenced specifi-

cally by molecular biological approaches. To investigate the impact of genetic approaches on

the formation of pellets and the pellet size, morphological measurement techniques shown in

Table 1 can be applied. However, the influence on the micromorphology of pellets can of-

14

ten not be determined. For example, hyperbranching can be quantified for dispersed hyphae

based on image analysis, while such methods do not exist for pellets so far.

Process engineering Several review articles describe process engineering approaches for

altering the morphology of filamentous fungal pellets (Böl et al., 2021; Krull et al., 2010,

2013; Veiter et al., 2018). Due to space limitation, only a small overview is presented about

approaches concerning inoculation, medium composition, and fluid dynamics.

Inoculation strategies are known for their high impact on the morphological development

(Prosser and Tough, 1991; Veiter et al., 2018). Papagianni and Mattey (2006), e.g., inocu-

lated bioreactors with A. niger spores in concentrations ranging from 104 to 109 spores per

milliliter and observed a clear transition from pelleted to dispersed macromorphologies. Con-

trary to A. niger (coagulative pellet formation type), non-coagulative pellet formation type

R. stolonifer (synonym R. nigricans) develops larger pellets at lower spore concentrations

(Žnidaršic et al., 2000). Besides inoculation with spores, inoculation with pellets can be a

promising strategy for A. niger cultivations (Wang et al., 2017).

The composition of the medium offers numerous opportunities to influence the morphol-

ogy. Besides traditional approaches such as the variation of pH (Priegnitz et al., 2012) and

nutrient-sources (Papagianni et al., 1999), two approaches are currently coming into focus:

the adjustment of the osmolality (Böl et al., 2021; Wucherpfennig et al., 2011) and the addi-

tion of particles (Böl et al., 2021; Karahalil et al., 2019). Wucherpfennig et al. (2011) showed

that A. niger pellets decrease in size with increasing osmolality. The addition of micropar-

ticles (diameter mostly < 50 µm (Böl et al., 2021)) can also reduce the size of filamentous

pellets and increase enzyme production (Antecka et al., 2016; Karahalil et al., 2019).

According to Krull et al. (2013), the reactor geometry, stirrer shape and size, and dissipated

energy are among the fluid dynamic-related criteria affecting the morphology and productiv-

ity in stirred tank reactors (STR). They concluded that low power input leads to inadequate

nutrient distribution and gas dispersion, whereas high power input can result in cell wall dam-

age. Consequently, high mechanical forces can result in chipping off hyphae from pellets (Cui

et al., 1997), which might reseed the fermentation broth. The following studies show that a

more profound understanding is required to correlate the power input with the morphology.

On the one hand, A. niger can grow to large pellets for low stirrer speeds, whereas high stir-

rer speeds can result in dispersed hyphae (El-Enshasy et al., 2006). On the other hand, an

increased mechanical power input can increase the density of the pellet periphery of A. niger

(Lin et al., 2010). The authors concluded that the increased density of the pellet periphery

might limit the mass transport of nutrients. Compared to STR, other reactor types such as air

lift column reactors (Gibbs et al., 2000; Xin et al., 2012) and rocking motion reactors (RMR)

(Kurt et al., 2018) can reduce shear stress. According to Kurt et al. (2018), RMR can result

in higher growth rates and more pelletized A. niger structures than STR.

The mentioned process engineering approaches offer numerous opportunities for targeted

morphological engineering. In particular, they enable the cultivation of predominantly pel-

letized or dispersed morphologies and affect the size of pellets. Some studies even showed the

15

possibility to alter the density of the pellet periphery, which could contribute as a diffusion

barrier. However, the impact of process engineering approaches on the micromorphology

within pellets has not yet been examined, which is caused by a lack of appropriate methods.

2.3.2 Modeling approaches

Several authors emphasize the demand for mechanistic modeling in order to predict the mor-

phological development for altered cultivation conditions, to reduce elaborate empirical tests,

and to improve the fundamental understanding between morphology and productivity (Celler

et al., 2012; Grimm et al., 2005; King, 1998; Posch et al., 2013; Veiter et al., 2018). In this

thesis, morphological modeling of filamentous pellets is categorized in 1) microscopic ap-

proaches, 2) continuum approaches, and 3) population balance modeling (PBM) approaches.

Microscopic approaches describe the growth of pellets, considering all positions of hyphae,

branches, and tips. Contrary, continuum approaches are less detailed and outline the ra-

dial distributions of morphological properties in pellets. While microscopic and continuum

approaches predict the development of individual pellets, PBM considers the pellet hetero-

geneity within a cultivation. As this thesis is based on the morphological characterization of

individual pellets, PBMs are not elaborated here. However, Section 6.3 includes a discussion

on how such modeling approaches could benefit from the methods and findings of this thesis.

Microscopic approaches As shown in Figure 4, microscopic models describe the devel-

opment of hyphal networks including the location of hyphae, tips, and branches. While two-

dimensional approaches consider the growth of filamentous microorganisms on a plane, three-

dimensional ones enable the simulation of hyphal networks in submerged cultures. Since this

thesis is about filamentous pellets, only three-dimensional models that incorporate the simu-

lation of whole pellets are considered here.

Based on stochastic rules for tip extension and branching, pellets can be simulated starting

from a single spore (Celler et al., 2012; Lejeune and Baron, 1997; Meyerhoff et al., 1995;

Yang et al., 1992a). For this, microscopic approaches considered following intracellular phe-

nomena: septation of hyphae (Celler et al., 2012; Yang et al., 1992a), distinction into apical,

subapical, and hyphal compartments (Celler et al., 2012), and consumption and flow of a com-

ponent in hyphae that influences the tip extension rate (Yang et al., 1992a). Recent advances in

measuring and modeling the intracellular transport of secretory vesicles, which transport cell

wall components to the hyphal tips (King, 2015; Kunz et al., 2020), have not been included

in three-dimensional microscopic pellet models yet. Contrary, several approaches considered

the diffusive mass transport of nutrients from the cultivation broth through the hyphal network

of pellets (Celler et al., 2012; Lejeune and Baron, 1997; Meyerhoff et al., 1995). For this, the

authors assumed spherical symmetry and computed the transport and consumption of nutri-

ents based on partial differential equations. To prevent hyphae from growing into each other,

collision detection can be included (Celler et al., 2012). Another phenomenon that can be

considered in microscopic models is the abrasion of pellets due to shear forces (Celler et al.,

2012; Meyerhoff et al., 1995). However, the development of coagulative pellets has not been

16

addressed sufficiently yet. While only Lejeune and Baron (1997) considered the development

of pellets from spore agglomerates, these simulations were limited to 100 randomly placed

spores. Hence, this was not realistic for coagulative pellet formation.

Most breakthroughs of microscopic approaches were achieved in the nineties including

three-dimensional representation, intracellular processes, diffusive mass transport of nutri-

ents into pellets, and abrasion of pellets. However, stagnation in model development can be

observed. That might be caused by the absence of experimental data for model validation.

Especially the hyphal network of the pellet interior cannot be quantified sufficiently to com-

pare simulated and cultivated pellets (Sections 2.1.2 and 2.1.3). Additionally, the models lack

well-founded correlations between the structure and the diffusivity for the computation of the

nutrient supply (Section 2.2.1).

Figure 4: Morphological modeling of pellets. Microscopic approach: own work based onCeller et al. (2012); Continuum approach: own work based on Buschulte (1992).

Continuum approaches First continuum approaches to model pellet growth were based

on the cube root relation for the development of the fungal biomass concentration in culti-

vations (Emerson, 1950; Pirt, 1966). The cube root relation is based on the hypothesis that

pellet growth occurs only in the periphery. Contrary, the pellet center is assumed to consist

of non-growing mycelium, into which oxygen does not diffuse. In later studies, the oxygen-

limitation inside pellets was confirmed experimentally (Cronenberg et al., 1994; Hille et al.,

2005; Wittier et al., 1986). Additionally, image analysis of pellet slices revealed the spatial

heterogeneity of the hyphal material inside pellets qualitatively (Hille et al., 2005; Lin et al.,

17

2010; Priegnitz et al., 2012). However, the cube root relation does not consider spatial hetero-

geneities of the hyphal fraction inside pellets. Buschulte (1992) and Meyerhoff et al. (1995)

overcame this limitation. Their approaches assumed spherical symmetry of pellets concern-

ing the spatial distribution of hyphal material and nutrients (Figure 4). Similar to microscopic

approaches (Celler et al., 2012; Lejeune and Baron, 1997), transport and consumption of

oxygen inside pellets was computed based on partial differential equations. In this way, the

inactivation of mycelial growth in the pellet center can be addressed based on the nutrient

profile. According to King (1998), a description with continuous variables for the biomass,

such as concentrations of hyphae and tips seems meaningful. The approach introduced by

Buschulte (1992) considers the radial concentrations of hyphae, tips, oxygen, and other sub-

strates inside pellets during their growth and is based on coupled partial differential equations

for these concentrations. With a so called layer model, Meyerhoff et al. (1995) described a

simplification of the approach of Buschulte (1992). This approach divides the pellet in a few

spherical shells and assumes constant values for hyphal fraction, tips, and nutrients inside

these shells. To reduce computational time, this model intentionally omits partial differential

equations except for the transport of nutrients into the pellet. Compared to a microscopic

model similar to Yang et al. (1992a), the continuum approach resulted in an about 60 - 100

fold reduction of the demands for computing capacity (Meyerhoff et al., 1995).

While the computational time of continuum approaches is lower compared to microscopic

ones, the level of detail remains high. Especially the morphological development of spherical

symmetric pellets can be well described. Although continuum approaches seem promising

to optimize filamentous fungal bioprocesses, recent advances are missing. To the author’s

knowledge, the model of Buschulte (1992) is still the most detailed approach. Similar to

microscopic approaches, continuum ones lack sufficient validation procedures, which might

be the reason for the stagnation in model development. Validation procedures would require

radial profiles of morphological properties and substrates and a well-founded law for the

diffusive mass transport through filamentous fungal networks. However, these properties are

difficult or even impossible to measure with current techniques (Sections 2.1.2, 2.1.3, and

2.2.1).

18

3 Problem definition

Although pellets are often exploited in industrial processes using filamentous fungi, their

inner structure and the resulting diffusion barrier for nutrients, oxygen, and secreted metabo-

lites remained largely unexplored. The following knowledge gaps regarding the micromor-

phology and diffusivity of filamentous fungal pellets were identified based on the theoretical

background.

Method to analyze the micromorphology of whole intact pellets does not exist.

The micromorphology within pellets is known to have a high impact on the productivity

of bioprocesses using filamentous fungi. Although many methods have been developed to in-

vestigate the macromorphology and periphery of pellets, there is no non-destructive approach

to visualize the three-dimensional micromorphology of whole pellets. Further, no method ex-

ists for the analysis of 3D images of filamentous fungal networks. Methods to visualize and

analyze the micromorphology of whole intact pellets would open new paths towards morpho-

logical engineering. For example, the impact of genetic and process engineering approaches

on the morphology of pellets could be investigated in utmost detail. Additionally, existing

morphological modeling approaches without suitable micromorphological input from exper-

iments could be validated and improved.

Correlation between the three-dimensional structure and the diffusivity of pellets is

not described. The supply with nutrients and oxygen is crucial for the metabolic activity

and product formation in pellets. Studies revealed that the transport of nutrients and oxygen

through dense hyphal networks is mainly driven by diffusion. However, a well-founded cor-

relation between the micromorphology and the diffusivity through fungal pellets is lacking in

literature. Such a correlation would enable the prediction of the diffusive transport of nutri-

ents, oxygen, and secreted metabolites in filamentous fungal pellets and thus, contribute to

the targeted design of pellet morphologies.

19

4 Methods for problem solving

The problem definition illustrates that new methods are required to reveal the micromor-

phology and diffusivity of filamentous pellets. Therefore, the following methods have been

developed. A detailed description of all methods can be found in the embedded papers.

Method to visualize whole intact pellets three-dimensionally. Applying X-ray mi-

crocomputed tomography (µCT) measurements, it became feasible to visualize the three-

dimensional (3D) network of hyphae forming filamentous fungal pellets. While this technique

enabled the non-destructive visualization of whole pellets with several hundred micrometers

in diameter, the hyphae with diameters down to 3 µm were resolved.

Method to analyze three-dimensional images of pellets. To quantify the micromor-

phology of whole pellets, automated image analysis was conducted on the acquired µCT

images. After binarization of the hyphal network, the centerlines of hyphae were determined

and used to locate tips and branches. This procedure enabled the investigation of morpholog-

ical properties such as the hyphal length, number of tips, number of branches, hyphal growth

unit (HGU), and porosity of whole pellets. Additionally, the spatial distributions of the hyphal

fraction, tip density, and branch density were determined.

Method to correlate structure and diffusivity of pellets. Diffusion computations were

conducted through numerous representative sub-volumes per µCT measured pellet. The com-

putations resulted in a diffusivity for each sub-volume, which is a measure for the geometrical

diffusion hindrance and independent of the diffusing substance. Correlation analysis between

the diffusivities and the structures of several hundred Aspergillus niger sub-volumes unveiled

a diffusion-law with respect to the solid hyphal fraction.

Method to determine a universal law for the diffusion through mycelial networks.

To consider the broad morphological range of filamentous fungi, the structures and diffu-

sivities of both µCT measured and simulated pellets were correlated based on the method

described above. While µCT measured pellets from four fungal species already showed

strongly differing morphologies, Monte Carlo simulated pellets covered the broad morpho-

logical range of filamentous microorganisms. To obtain the required 3D structures of the

simulated pellets, an existing microscopic model was extended and implemented. Analysis

of all measured and simulated pellets unveiled a universal law for the diffusion of nutrients,

oxygen, and secreted metabolites with the solid hyphal fraction as the only independent vari-

able.

20

5 Results

5.1 Paper I: An X-ray microtomography-based method for

detailed analysis of the three-dimensional morphology of

fungal pellets (Schmideder et al., 2019a)

Summary

Although the micromorphology of filamentous fungal pellets is strongly linked to the produc-

tivity in bioprocesses, there is no method to visualize the detailed three-dimensional morphol-

ogy of whole intact pellets. Further, no method for the analysis of three-dimensional images

of filamentous fungal networks exists to date. To enable the non-destructive visualization of

whole pellets, we developed a protocol based on X-ray microcomputed tomography (µCT).

Exemplarily, we investigated pellets of Aspergillus niger and Penicillium chrysogenum. The

binarization of the images enabled the determination of the hyphal network within whole pel-

lets. Based on the binarized hyphal network, skeletonization was conducted to investigate the

location of tips and branches as well as the total hyphal length. Thus, the cumulative mor-

phological properties total hyphal length, total tip number, total branch number, porosity, and

hyphal growth unit of whole pellets can be determined. Additionally, multiple hypotheses

about the morphological development of fungal pellets can be drawn from the spatial distri-

butions of the hyphal fraction, tip density, and branch density. Based on µCT measurements

and image analysis, the outcome of experimental morphological engineering approaches on

pellet structures can be investigated in unprecedented detail. Further, the determined three-

dimensional morphology will serve as valuable input to validate and improve existing mor-

phological modeling approaches. As shown in Paper II and III, the structure of analyzed

pellets can also be used to compute the resulting diffusion barrier for nutrients, oxygen, and

secreted metabolites.

Author contributions

Stefan Schmideder did the conception and design of the study and wrote the manuscript,

which was edited and approved by all authors. Heiko Briesen and Vera Meyer supervised the

study. Lars Barthel and Ludwig Niessen cultivated and freeze-dried fungal pellets. Stefan

Schmideder and Michaela Thalhammer developed a protocol for µCT measurements. Stefan

Schmideder, Tiaan Friedrich, and Tijana Kovacevic developed 3D image analysis of µCT

measurements. Stefan Schmideder analyzed the results. Stefan Schmideder, Lars Barthel,

Heiko Briesen, and Vera Meyer interpreted the results.

21

Received: 14 August 2018 | Revised: 21 December 2018 | Accepted: 9 January 2019

DOI: 10.1002/bit.26956

AR T I C L E

An X‐ray microtomography‐based method for detailedanalysis of the three‐dimensional morphologyof fungal pellets

Stefan Schmideder1 | Lars Barthel2 | Tiaan Friedrich1 | Michaela Thalhammer1 |Tijana Kovačević1 | Ludwig Niessen3 | Vera Meyer2 | Heiko Briesen1

1Technical University of Munich, School of Life

Sciences Weihenstephan, Chair of Process

Systems Engineering, Freising, Germany

2Department of Applied and Molecular

Microbiology, Institute of Biotechnology,

Technische Universität Berlin, Berlin,

Germany

3Lehrstuhl für Technische Mikrobiologie,

Technical University of Munich, Freising,

Germany

Correspondence

Heiko Briesen, Technical University of

Munich, Gregor‐Mendel‐Straße 4, 85354

Freising, Germany.

Email: [email protected]

Funding information

Deutsche Forschungsgemeinschaft, Grant/

Award Numbers: BR 2035/11‐1, ME 2041/5‐1, DFG INST 95/1111‐1, BR 2035/11‐1 and

ME 2041/5‐1

Abstract

Filamentous fungi are widely used in the production of biotechnological compounds.

Since their morphology is strongly linked to productivity, it is a key parameter in

industrial biotechnology. However, identifying the morphological properties of

filamentous fungi is challenging. Owing to a lack of appropriate methods, the

detailed three‐dimensional morphology of filamentous pellets remains unexplored. In

the present study, we used state‐of‐the‐art X‐ray microtomography (µCT) to develop

a new method for detailed characterization of fungal pellets. µCT measurements were

performed using freeze‐dried pellets obtained from submerged cultivations. Three‐dimensional images were generated and analyzed to locate and quantify hyphal

material, tips, and branches. As a result, morphological properties including hyphal

length, tip number, branch number, hyphal growth unit, porosity, and hyphal average

diameter were ascertained. To validate the potential of the new method, two fungal

pellets were studied—one from Aspergillus niger and the other from Penicillium

chrysogenum. We show here that µCT analysis is a promising tool to study the three‐dimensional structure of pellet‐forming filamentous microorganisms in utmost detail.

The knowledge gained can be used to understand and thus optimize pellet structures

by means of appropriate process or genetic control in biotechnological applications.

K E YWORD S

filamentous fungi, image analysis, pellets, three‐dimensional morphological quantification, X‐raymicrotomography

1 | INTRODUCTION

Filamentous fungi are microorganisms with a high capability to produce

primary metabolites, proteins, secondary metabolites, and biopolymers.

Over a century of research on filamentous fungi has led to the

development of diverse biotechnological applications, including the

production of organic acids, enzymes, antibiotics, and exopolysaccharides

(Cairns, Nai, & Meyer, 2018; Meyer, 2008; Meyer et al., 2016). When

filamentous fungi are cultivated in a submerged culture, they develop

different macromorphologies, such as dispersed mycelia consisting of

nonaggregated hyphae, clumps of loosely aggregated hyphae, and densely

packed compact spherical structures called pellets (Pirt, 1966). Such

morphology is determined by the fungal species and the cultivation

conditions, including the fermenter geometry, agitation systems, cultiva-

tion mode (batch, fed‐batch, or continuous), type and concentration of

substrates, pH, and temperature (Papagianni, 2004). The preferable

fungal morphology strongly depends on the aim of the respective

bioprocess (Gibbs, Seviour, & Schmid, 2000). For example, the industrial

cell factory Aspergillus niger is used in its pellet form to produce citric acid

and in its dispersed form to produce enzymes (Meyer et al., 2016).

Biotechnology and Bioengineering. 2019;1-11. wileyonlinelibrary.com/journal/bit © 2019 Wiley Periodicals, Inc. | 1

22

Because fungal morphology is of considerable importance, it is

vital to thoroughly study the structure of hyphal aggregates. Light

microscopy is sufficient enough to analyze and characterize disperse

mycelium and small aggregates owing to their simple geometry.

However, more sophisticated tools are essential for analyzing the

complex morphology of densely packed pellet structures. The inner

pellet region often differs from its outer region. Densely packed

pellets result in oxygen limitation in the inner region, thereby making

the pellets prone to reduced growth or even autolysis (Ehgartner,

Herwig, & Fricke, 2017; Hille, Neu, Hempel, & Horn, 2006). Many

techniques have been developed to study the inner pellet region. A

relatively simple method is the analysis of pellet slices by using light

microscopy (Lin, Scholz, & Krull, 2010). A more advanced technique

for the same purpose is the use of confocal laser scanning

microscopy. By using this technique, cryomicrotome slices of

previously frozen and dyed fungal pellets, with a thickness of

40–60 µm, are scanned three‐dimensionally and then evaluated with

image analysis, giving a hyphal distribution for small cutouts of the

pellet (Hille, Neu, Hempel, & Horn, 2005). Applying viability staining

in combination with confocal laser scanning microscopy, active and

inactive pellet regions can be detected (Nieminen, Webb, Smith, &

Hoskisson, 2013). Further information can be obtained using cryo‐scanning electron microscopy with whole pellets, revealing the

difference between highly intertwined superficial hyphae and a

densely packed deep mycelium (Villena & Gutiérrez‐Correa, 2007). Inaddition to these single‐sample examination methods, flow cytome-

try can be used to elucidate the core compactness of numerous

fungal pellets in short time (Ehgartner et al., 2017).

In fungal biotechnology, three pellet‐forming mechanisms are

generally distinguished: coagulative, noncoagulative, and hyphal

element agglomerating (Veiter, Rajamanickam, & Herwig, 2018).

Coagulative formation comprises two steps. Numerous spores

aggregate because of electrostatic and hydrophobic interactions

and then the aggregated spores begin to germinate and form pellets

(Zhang & Zhang, 2016). A typical representative of this is A. niger. In

noncoagulative formation, the spores germinate before they start to

form pellets, meaning that, theoretically, a single spore forms a pellet.

Species that commonly form noncoagulative pellets include Rhizopus

oryzae and Mortierella vinacea (Zhang & Zhang, 2016). Some fungi,

such as Penicillium chrysogenum show both, coagulative and non-

coagulative pellet formation, and are therefore categorized into the

hyphal element agglomerating type. In this case, the agglomeration of

different hyphal elements leads to hyphal clumps and subsequent

pellet formation (Veiter et al., 2018).

Modeling approaches have been developed to predict the

morphology of filamentous pellets in submerged cultures (King,

1998, 2015; Meyer, Fiedler, Nitsche, & King, 2015). Many modeling

approaches include locating the hyphae, tips, and branches in

filamentous pellets (Celler, Picioreanu, vanLoosdrecht, & vanWezel,

2012; Lejeune & Baron, 1997; Yang, King, Reichl, & Gilles, 1992).

Others assume spherical symmetry of pellets and consider morpho-

logical properties, such as the hyphal length density and tip density

dependent on the radius (Buschulte, 1992; Meyerhoff, Tiller,

& Bellgardt, 1995). However, these modeling approaches have not

been fully validated yet owing to the significant lack of knowledge of

three‐dimensional pellet morphologies.

This study thus introduces a new method for a detailed

investigation of the morphological properties of filamentous pellets

and is structured as follows: In Section 2, the preparation of fungal

pellets and the microtomography (µCT) measurements are described.

The applied µCT measurements offer a nondestructive way to

visualize complex morphologies and are applied intensively in

medical and biological research as well as material science (Salvo

et al., 2003; Stock, 2008). Since the subsequent data processing of

fungal pellets cannot be clearly separated into the methodological

development of the image processing and the results of this

processing, Section 3 is introduced. By applying three‐dimensional

image analysis, the locations of hyphae, tips, and branches were

determined. To demonstrate the potential of the described method,

two freeze‐dried fungal pellets from submerged cultivations from A.

niger and P. chrysogenum, respectively, were investigated in detail in

the Section 4. Based on the processed data of the fungal pellets,

morphological properties like the hyphal length, number of tips,

number of branches, hyphal growth unit (HGU), porosity, and

average diameter of hyphae were investigated.

2 | MATERIALS AND METHODS

2.1 | Pellet preparation

Conidiospores of P. chrysogenum strain MUM17.85 (Micoteca da

Universidade do Minho, Braga, Portugal) and A. niger strain MF22.4

(Fiedler, Barthel, Kubisch, Nai, & Meyer, 2018) were obtained from

agar plate cultures by using standard procedures for filamentous

fungi (Bennett & Lasure, 1991). The spores were grown in liquid

cultivation media for P. chrysogenum (yeast carbon base; Difco,

Franklin Lakes, NJ) and A. niger (complete medium; Meyer, Ram, &

Punt, 2010) for 24–48 hr until pelleted structures became visible.

Single pellets were then carefully removed by pipetting and were

washed three times with water. Samples were frozen in liquid

nitrogen while pellets were floating in water to preserve their

structure and were subsequently freeze‐dried. A FreeZone device

(Labcono, Kansas City, MO) was used to freeze dry the A. niger pellet

at 0.014 mbar and −55°C for 24 hr. The freeze‐drying of the P.

chrysogenum pellet was performed using a FreeZone 2,5 PLUS device

(Labconco) at 0.002 mbar and ambient temperature for 24 hr. To

prevent the freeze‐dried pellets from absorbing water, the samples

were stored in sealed Eppendorf tubes for further use. To investigate

the influence of the applied freeze‐drying process on the morphology

of filamentous pellets, we compared the same pellets in two states:

wet (immediately after fermentation) and freeze‐dried. Light micro-

scope images of wet and freeze‐dried A. niger and P. chrysogenum

pellets are shown in Figures S1–S5. After 48 hr fermentation of A.

niger and P. chrysogenum, the diameter of freeze‐dried pellets

decreased by 9% and 10% on average, respectively. The pellet

diameter has been calculated on base of the outermost hyphae of the

2 | SCHMIDEDER ET AL.

23

pellets. The fermentation of P. chrysogenum for 24 hr resulted in

looser pellets (Figure S3) and a decrease in the dried pellet diameter

of 13%. In addition, we measured the diameter of wet and freeze‐dried hyphae at the pellet periphery of P. chrysogenum pellets

manually with FIJI. The average diameter of wet hyphae was 3.6 µm,

whereas freeze‐dried hyphae had an average diameter of 3.5 µm. In

addition, the freeze‐dried samples do still exhibit hairy regions in the

outer part of the pellets (Figures S4 and S5).

2.2 | X‐ray microtomography

Three‐dimensional images of the fungal pellets were acquired using a

custom‐built X‐ray microtomography system (XCT‐1600HR; Matrix

Technologies, Feldkirchen, Germany). Between the open tube and

the detector, the fungal pellets were fixed on a sample holder, which

rotated during the measurement. The tube of the µCT system

generates a cone beam. Thus, two‐dimensional projections were

obtained from various angles. The projections were reconstructed

using a custom‐designed software (Matrix Technologies) that uses

CERA (Siemens, Munich, Germany) to receive three‐dimensional

images. Because freeze‐dried filamentous pellets have a low density,

low energy (60 kV, 25 µA) was used to generate the cone beam. The

three‐dimensional images had a resolution of 1 µm (i.e., the edge

length of the voxels was 1 µm). To fix the A. niger pellet on top of the

sample holder, an instant adhesive (UHU, Bühl, Germany) was used.

Partial embedding of the A. niger pellet in the instant adhesive

guaranteed structural stability. For the P. chrysogenum pellet, a

double‐sided tape (Tesa, Norderstedt, Germany) was sufficient to

guarantee structural stability.

3 | DATA PROCESSING

This section describes the detection of tips, branches, and hyphal

material in pellets by using image analysis. The analysis was

conducted with the µCT images of the A. niger (Figure 1) and the P.

chrysogenum pellet (Figure 2) acquired as described in Section 2.

3.1 | Preprocessing

Preprocessing aimed to generate binarized three‐dimensional images

with the hyphal material as foreground. Thereby, voxels originating

from noisy data and sample fixation materials must be separated

from the pellet.

Both fixation materials, the instant adhesive for A. niger and the

double‐sided adhesive tape for P. chrysogenum, showed gray values

similar to those of the pellets. Because of this, the automated

segmentation of the pellet turned out to be difficult to implement. To

achieve successful segmentation, the images were cropped. Part of

the A. niger pellet enclosed in the instant adhesive was deformed. For

further investigation, a conically shaped section was cropped from

the raw data using MATLAB (version R2016a; MathWorks, Natick,

MA), resulting in a structure not affected by the fixation material

(Figure 1a). This cone was used to represent the whole pellet.

According to visual observations, the tip of the cone was assumed to

be the center of the pellet. The opening angle of the cone was chosen

to be 65°. The P. chrysogenum pellet was cropped by cutting off a

small XY‐orientated slice at the bottom of the three‐dimensional

image with the software MAVI (version 1.4.1; Fraunhofer ITWM,

Kaiserslautern, Germany). After cropping, the 16‐bit grayscale

F IGURE 1 µCT image of A. niger pellet;two‐dimensional projections of a

three‐dimensional image. (a) Whole pelletwith XZ‐orientation; red object representsthe analyzed cone of the pellet;transparent white object represents the

remaining pellet and fixation material.(b–d) Slices (100 µm) of differentorientations; center of the slices is the

pellet center; image processed with basicrendering only; (b) XY‐orientation;(c) YZ‐orientation; (d) XZ‐orientation[Color figure can be viewed atwileyonlinelibrary.com]

SCHMIDEDER ET AL. | 3

24

images (i.e., voxels of µCT images exhibiting gray values between 0

and 65,535) were binarized to differentiate between the hyphae and

background (Figure 3a,b). The binarization was performed using

MAVI by setting a gray value threshold that was calculated using

Otsu’s method (Otsu, 1979). The voxels with gray values higher than

the gray value threshold were designated as hyphal material. Small

interconnected objects, which were not part of the pellet, were

eliminated. This was achieved by labeling neighboring voxels with

MAVI and deleting all but the largest object. It has to be mentioned

that MATLAB or FIJI could also be applied to the preprocessing steps

conducted in MAVI. However, the three‐dimensional rendering

performance of MAVI was highly superior, which enabled to visualize

the conducted processing steps immediately.

3.2 | Skeletonization

Since there exists no established three‐dimensional skeletonization

method for filamentous microorganisms, we adopted and adapted a

procedure that has been already successfully applied for two‐dimensional image analysis. Barry, Williams, and Chan (2015)

published an ImageJ plugin for the morphological analysis of light

microscope images of filamentous microorganisms. In their two‐dimensional skeletonization procedure, they also applied an iterative

thinning method, as we chose for our three‐dimensional skeletoniza-

tion. An advantage of the usage of an iterative thinning algorithm is

its computational efficiency. Skeletonization alternatives, such as

methods based on Voronoi Covariance Measurement (Grélard,

Baldacci, Vialard, & Domenger, 2017) would result in significantly

higher computation times. However, computational efficiency is

crucial for the analysis of the high data volume of the µCT

measurements. In the present work, skeletonization was achieved

using the plugin “Skeletonize (2D/3D)” for FIJI/ImageJ (Schneider,

Rasband, & Eliceiri, 2012; Schindelin et al., 2012). This plugin is based

on the three‐dimensional thinning algorithm by Lee, Kashyap, and

Chu (1994) and Homann (2007). The basic procedure is to erode the

object’s surface iteratively until only the centerline remains. To

analyze the obtained skeleton voxels of the three‐dimensional image,

the FIJI plugin “Analyze Skeleton (2D/3D)” (Arganda‐Carreras,Fernández‐González, Muñoz‐Barrutia, & Ortiz‐De‐Solorzano, 2010)was used. Depending on their direct neighbors, the skeleton voxels

can be categorized into three different classes: tips, “normal” hyphae,

and branch voxels. The tips are endpoints of the skeleton with only

one neighbor. “Normal” hyphae are skeleton voxels with two

neighbors, and branch voxels are skeleton voxels with at least three

neighbors. As illustrated in Figure 3c,d, the plugin labels each voxel of

the skeleton as either a hyphal voxel (red), a branch voxel (green), or

a tip (yellow). In addition, the plugin calculates the total hyphal length

of the pellet based on the number and location of skeleton voxels.

3.3 | Postprocessing

To correct minor issues arising because of preprocessing and

skeletonization, three postprocessing steps were applied to the

skeleton using MATLAB.

The first issue concerns incorrect short junctions, appearing due

to surface roughness (Figure 4a,b). The deletion of such short

junctions is a commonly described issue when working with skeletons

(e.g. Barry, Chan, & Williams, 2009; Grélard et al., 2017). To delete

F IGURE 2 µCT image of a P.chrysogenum pellet; two‐dimensional

projections of three‐dimensional image;slices (100 µm) of different orientations;center of the slices is the pellet center;image processed with basic rendering only.

(a) XY‐orientation; (b) YZ‐orientation; (c)XZ‐orientation

4 | SCHMIDEDER ET AL.

25

such junctions, geodesic distance transform (MATLAB function

“bwdistgeodesic”) was used, which can measure the distance

between a pair of voxels obtained by traversing only the foreground

voxels. Here, the distance was measured as quasi‐Euclidean,

approximating the actual distance between each pair of the

neighboring voxels on the path. First, this procedure ascertained

the distance ,xmin branch to the closest branch voxel for each hyphal

(skeleton) voxel. Afterward, the procedure was used to find the

F IGURE 3 Image processing steps for a

small region of the P. chrysogenum pellet;images are rendered with VGSTUDIOMAX. (a) Raw image: CT data with a low

threshold for gray values. (b) Preprocessedimage: for binarization, threshold for grayvalues is applied; additionally, small

connected objects are deleted. (c)Skeletonized image. (d) Analyzed image:analysis of the skeleton; tips are markedyellow and branches green [Color figure

can be viewed at wileyonlinelibrary.com]

F IGURE 4 Postprocessing steps forsmall regions of P. chrysogenum pellet;transparent white objects illustrate thebinarized three‐dimensional data, red

objects the skeleton, yellow markers thetips, and green markers the branches. (a)Without postprocessing: coarse surface of

binarized hyphae results in short junction.(b) Postprocessing: short junction resultingfrom coarse surface of binarized hyphae is

deleted. (c) Without postprocessing:overlapping hyphae result in branch. (d)Postprocessing: incorrect branch is

deleted. (e) Without postprocessing: closeparallel hyphae can cause bridges imitatingbranches. (f) Postprocessing: incorrectbranches are deleted [Color figure can be

viewed at wileyonlinelibrary.com]

SCHMIDEDER ET AL. | 5

26

distance ,xmin tip to the closest tip voxel. After this,

= +, + , ,x x xsum tip branch min tip min branch for each voxel of the skeleton

was calculated. Tip and “normal” hyphae voxels of the skeleton with

≤, +x xsum tip branch threshold were deleted. Branch voxels of the skeleton

with ≤, +x xsum tip branch threshold were changed to “normal” hyphae

voxels. With 4 µm, xthreshold was set to a value close to the hyphal

diameter (Nielsen, 1993; Packer, Keshavarz‐Moore, Lilly, &

Thomas, 1992).

In addition, overlapping hyphae misleadingly resulted in branches.

This could be easily corrected because overlapping hyphae result in

four hyphal tubes, whereas a true branching hypha generates three

hyphal tubes connected to the branch (Figure 4c,d). Hence, the

number of hyphal tubes connected to the branch were counted, and a

branch was defined as correct, only if it was connected to three

hyphal tubes.

Binarization of close parallel hyphae may occasionally be

misinterpreted as branches because of small bridges between the

hyphae. The connection between two parallel hyphae can be caused

by two effects: the fusion between hyphae (Read & Lichius, 2009) or

misinterpreting noisy data by image analysis. The investigation of the

actual origin could be the focus of future studies. In both cases, the

branches are not caused by branching itself. Hence, the last

postprocessing step changed the incorrect branches to “normal”

hyphae (Figure 4e,f). Branches closer to another branch at a distance

of less than 6.5 µm (P. chrysogenum) or 5.5 µm (A. niger) were defined

as incorrect. These thresholds were chosen to be 2 µm higher than

the average hyphal diameters (Nielsen, 1993; Packer et al., 1992).

Overall, this processing step prevented an overestimation of the

number of branches.

3.4 | Determination of the local hyphal fraction

The newly defined morphological property, “local hyphal fraction”

(LHF), is a measure of the local accumulation of hyphal material in

filamentous pellets. The LHF is the ratio between the volume of

hyphal material and the total volume with regard to a specified local

volume. Binarized images of the pellets included hyphal voxels and

voxels corresponding to empty space. The LHF was determined by

applying an appropriate filter to the binarized images. For each voxel,

the filter counted the hyphal voxels in its neighborhood. To obtain an

average of the neighborhood, a cube with an edge length of 61 voxels

was used, with the center of the cube containing the target voxel.

The LHF of a voxel is the number of hyphal voxels of the cube divided

by the total number of voxels of the cube. Thus, a voxel with an LHF

of 0.3 implies that the region of the target voxel has a porosity of

70%, and the remaining 30% of the region is filled with hyphal voxels.

Applying this filter method, the LHF of each pellet voxel was

calculated.

To enable visualization of the LHFs at different points, these

values are shown on spherical shells with varying radius. For each

sphere, the LHFs are shown on 4,800 equally‐distributed points, as

illustrated in Figure 9. The points were obtained by the HEALPix

discretization (Gorski et al., 2005), which provides 4,800 representa-

tive coordinates at the sphere surface. Thus, the value of the LHF of

the closest voxel of the pellet was assigned to the representative

coordinate of the sphere.

4 | RESULTS AND DISCUSSION

In this study, we demonstrate the potential of our µCT measurement

and three‐dimensional image analysis system to investigate the

morphology of filamentous pellets. Exemplarily, two pellets have been

investigated in detail: one A. niger (Figure 1) and one P. chrysogenum

(Figure 2) pellet. A. niger represents the coagulative type for pellet

formation and P. chrysogenum the hyphal element agglomerating type.

The investigation of the pellets is based on final binarized (Figure 3a,b),

skeletonized (Figure 3c,d), and post‐processed (Figure 4) pellets. The

F IGURE 5 Skeletonized region of

P. chrysogenum pellet: white transparentobject illustrates the binarizedthree‐dimensional data, red object the

skeleton, yellow markers the tips, andgreen markers the branches [Color figurecan be viewed at wileyonlinelibrary.com]

6 | SCHMIDEDER ET AL.

27

mentioned operation steps are described and discussed in detail in

Section 3. Figure 5 displays a processed region of the P. chrysogenum

pellet.

4.1 | Global morphology of pellets

The final processed images were used to calculate pellet diameter,

porosity, total hyphal length, average hyphal diameter, total tip

number, total branch number, HGU, and hyphal branch unit (HBU). In

the case of the A. niger pellet, a conical section of the pellet not

affected by the fixation material was analyzed (Figure 1a). To

determine the morphology of the whole pellet, the other part of the

pellet was assumed to exhibit the same properties as the studied

portion. This approach was selected because visual observation of

the A. niger showed spherical symmetry (Figure 1 and see below). As

the P. chrysogenum pellet was not affected by the fixation material, it

was possible to analyze the complete pellet.

The diameter of the pellet dPellet was estimated as the volume

equivalent diameter of the convex hull of the respective pellet:

π=

⋅d VPellet

6 ConvHull3 . The porosity, ϵ , was defined by the volume of the

hyphal material VHyphae and the volume of the convex hull of the

pellet: ϵ = −1V

VHyphae

ConvHull. The total hyphal length LHyphae, total tip

number, and total branch number were determined as described

earlier. Based on the volume of the hyphal material and the total

F IGURE 6 Regions with high hyphal

fractions of the cone of the A. niger pelletillustrated for three different perspectives;white: binarized cone of A. niger pellet;

yellow: regions with a hyphal fractionhigher than 0.20. (a) Bottom perspective.(b) Right perspective. (c) Front perspective

[Color figure can be viewed atwileyonlinelibrary.com]

F IGURE 7 Regions with high hyphal

fractions of P. chrysogenum pelletillustrated for three different perspectives;white: binarized P. chrysogenum pellet;

yellow: regions with a hyphal fractionhigher than 0.20. (a) Bottom perspective.(b) Right perspective. (c) Front perspective[Color figure can be viewed at

wileyonlinelibrary.com]

SCHMIDEDER ET AL. | 7

28

hyphal length, the average diameter of hyphae dHyphae was calculated

asπ

=⋅

⋅d V

LHyphae4 Hyphae

Hyphae. The HGU and HBU were estimated as

follows:

=HGUTotal hyphal length

Total number of tips(1)

=HBUTotal hyphal length

Total number of branches. (2)

The morphological properties of the analyzed A. niger pellet and

P. chrysogenum pellet are listed in Table 1. The A. niger pellet has a

diameter of 633 µm, a porosity of 0.87, and an average hyphal

diameter of 3.8 µm. The P. chrysogenum pellet has a diameter of

1085 µm, a porosity of 0.94, and an average diameter of 4.1 µm.

These diameters of the hyphae correspond to those described in

the literature (Colin, Baigorí & Pera, 2013; Morrison & Righelato,

1974; Nielsen, 1993; Packer et al., 1992). Since the average hyphal

diameter was calculated on the basis of the volume of the hyphal

material and the total hyphal length, our image data suggest that

they are sufficiently precise to deduce biologically meaningful

information. The HGU and HBU, respectively, were 95 µm and 93

µm for A. niger and 150 µm and 135 µm for P. chrysogenum.

Considering a single pellet, the HGU and HBU should be in a similar

range because each new branch results in one new tip. With 95 µm,

the A. niger pellet showed an HGU in a range comparable to literature

(Colin et al., 2013). By contrast, the P. chrysogenum pellet, with an

HGU of 150 µm, showed a higher HGU value than mentioned in the

literature (29–99 µm; Morrison & Righelato, 1974). The reported

value, however, has been obtained for disperse mycelia and loose

clumps and therefore cannot be directly compared with the present

study. Nevertheless, we emphasize that future studies involving µCT

measurements of fungal pellets need a large sample size for analysis

to obtain statistically significant data.

It is clear that µCT analysis is a powerful tool to estimate

morphological properties of fungal pellets, including total hyphal

length, total tip number, total branch number, HGU, and HBU. To our

knowledge, this is the first study to do so. Moreover, properties such

as porosity and average hyphal diameter can be estimated on the

basis of information obtained for a complete pellet. The determina-

tion of pellet’s porosity via light microscopic analysis of pellet cross

sections (Hille et al., 2005; Lin et al., 2010) was to date possible only

with low accuracy due to the thickness of the applied slices. Applying

confocal laser scanning microscopy (Villena, Fujikawa, Tsuyumu, &

0 100 200 300Radius, µm

0

0.05

0.1

0.15

0.2

0.25

0.3

Hyp

hal f

ract

ion,

-

(a)

0 100 200 300Radius, µm

0

1

2

3

4

5

Num

ber

of ti

ps/b

ranc

hes

per

volu

me,

10

5 m

m-3

TipsBranches

(b)

0 100 200 300Radius, µm

0

50

100

150

200

HG

U /

HB

U, µ

m

HGUHBU

(c)

F IGURE 8 Morphological properties of spherically symmetric A. niger pellet dependent on radius; morphological properties are calculatedfor shells. The width of shells is 25 µm and the inner sphere has a radius of 50 µm. (a) Hyphal fraction. (b) Number of tips/branches per volume.

(c) Hyphal growth unit (HGU): hyphal length in micrometer per number of tips; hyphal branch unit (HBU): hyphal length in micrometer pernumber of branches [Color figure can be viewed at wileyonlinelibrary.com]

F IGURE 9 Local hyphal fraction of P.chrysogenum pellet for different distancesfrom the pellet center: (a) 150 µm. (b)

250 µm. (c) 350 µm [Color figure can beviewed at wileyonlinelibrary.com]

TABLE 1 Morphological properties of the fungal pellets

A. niger P. chrysogenum unit

Diameter of pellet 633 1,085 µm

Porosity 0.87 0.94 –

Total hyphal length 1,472,998 2 995,557 µm

Average diameter of hyphae 3.8 4.1 µm

Total number of tips 15,425 20,000 –

Total number of branches 15,768 22,123 –

Hyphal growth unit 95 150 µm

Hyphal branch unit 93 135 µm

8 | SCHMIDEDER ET AL.

29

Gutiérrez‐Correa, 2010) or flow cytometry (Ehgartner et al., 2017),

only superficial parts of pellets have been investigated.

4.2 | Distribution of hyphal material within pelletstructures

Next, we checked whether the three‐dimensional distribution of fungal

biomass within a pellet can be used to deduce information about the

pellet’s genesis and development during submerged cultivation. To

determine the regions with a high biomass content, three‐dimensional

distribution of the LHF was calculated, as described in Section 3.4.

Subsequently, a threshold value for the LHF was set. As a result, only

the regions of the pellet with a higher LHF than the set threshold

remained.

The threshold for the hyphal fraction of the conical section of the

A. niger pellet was set to 0.20 (Figure 6), which was chosen to be close

to the maximum hyphal fraction. Two regions with high hyphal

fractions were observed: a smaller region in the pellet’s center and a

larger region in the outer part. The regions with high hyphal fractions

show spherical symmetry with the cone tip at the center, which was

reflected in Figure 1, confirming that the A. niger pellet was

spherically symmetric. The dense region in the pellet’s center was

possibly a result of agglomeration events involving the conidia and

germ tubes. These early agglomeration events are common pellet‐building mechanisms seen in filamentous microorganisms of the

coagulative type, including A. niger Zhang & Zhang, 2016.

With 0.20 as the threshold of the LHF of the P. chrysogenum pellet,

the value was also set close to the maximum LHF. Figure 7 shows three

regions with high hyphal fractions: one large region and two small ones.

Although the P. chrysogenum pellet on its own is spherical, no spherical

symmetry was visible for the location of the regions with high hyphal

fractions. Considering the three regions with high hyphal fractions, it

can be supposed that the P. chrysogenum pellet was a product of the

agglomeration of three hyphal clumps. This is a typical pellet‐formation

mechanism for filamentous microorganisms of the hyphal element

agglomerating type, including P. chrysogenum (Nielsen, Johansen,

Jacobsen, Krabben, & Villadsen, 1995; Veiter et al., 2018).

Our data show that analyzing hyphal fractions provides new

insights into the symmetry of fungal pellets and hypotheses can be

deduced with respect to their evolution. This knowledge can be used

to rationally engineer aggregation events by appropriate process

control and/or by genetic modifications to obtain final pellet

structures with improved productivities during industrial processes.

4.3 | Radial morphology of spherically symmetricpellets

Spherically symmetric pellets offer the opportunity to characterize

morphological properties along their radii. Thus, the morphological

properties of shells of the A. niger pellet were analyzed. Again, only a

cone of the pellet not affected by the fixation material was studied

(compare Figure 1a). To determine the morphology of the entire

pellet, the remainder part of the pellet was assumed to exhibit

properties identical to those of the cone. The width of shells was set

to 25 µm. The inner sphere had a radius of 50 µm. To determine the

hyphal fraction of a shell, the hyphal volume of the shell was divided

by the total volume of the shell. In addition, the number of branches

and tips per shell were divided by the total volume of shells. To

obtain the HGU and HBU, the hyphal length of the shells was divided

by the number of tips and branches.

Figure 8a shows that the hyphal fraction of the A. niger pellet

contained two maxima. One maximum was in the pellet center, and

the other one at a distance 200 µm outside the center. These

observations are in accordance with the investigation of the regions

with a high hyphal fraction in Section 4.2. Between the two maxima, a

local minimum with a hyphal fraction of about 0.15 could be

observed at 100–125 µm. Starting from the second local maximum at

200 µm, the hyphal fraction decreased, until the edge of the pellet

was reached at a radius between 300 and 325 µm.

With ⋅2.8 105 branches per mm3, the branching density was

highest at the pellet center. From there, the branching density

gradually decreased to ⋅1.9 105 branches per mm3 at a radius of

250 µm. Then, the branching density decreased rapidly toward the

edge of the pellet. With ⋅2.0 105 tips per mm3, the tip density had a

local minimum at the pellet center. From there, the tip density

increased until the maximum tip density of ⋅4.2 105 tips per mm3 was

reached between 100 and 125 µm. From there, the tip density

decreased towards the edge of the pellet.

HGU and HBU result from the hyphal length of shells and the

corresponding number of tips and branches. It is clear that HBU does

not vary strongly along the radius and has values between 80 and

120 µm. Therefore, it can be assumed that the number of branches is

directly proportional to the hyphal length for the whole pellet. By

contrast, the HGU varies strongly along the radius, which is why the

number of tips is not directly proportional to the hyphal length.

4.4 | Nonsymmetry of pellets

Finally, a method to detect and illustrate nonsymmetry of filamentous

pellets is presented. Exemplarily, the method was applied to the P.

chrysogenum pellet. Thereby, the LHF was calculated as described in

Section 3.4. The mass center of the pellet was calculated based on the

hyphal volume elements. By using the HEALPIX algorithm, the LHF for

different distances from the pellet center was determined. Figure 9

shows the LHFs for three different distances from the center.

As shown, the LHF varied strongly for all illustrated distances from

the pellet center. At a distance of 150 µm from the center, the LHF

varied between 0.075 and 0.15. At a distance of 250 µm, the range of

the LHF was between 0.075 and 0.3. At a distance of 350µm, the LHF

varied even more strongly, with values between 0 and 0.3.

4.5 | Critical evaluation of the µCT‐based method

The new method to determine morphological properties with µCT

measurements and subsequent three‐dimensional image analysis has

considerable benefits compared with existing methods. For the first

SCHMIDEDER ET AL. | 9

30

time, hyphal material, tips, and branches can be located and quantified

for entire filamentous pellets. Thus, it is also the first time, that the

following properties of entire pellets are reported: total hyphal length,

total tip number, total branch number, HGU, and the newly defined

parameter HBU.With the applied technique, the inner part of the fungal

pellet can be studied along with the outer part, which is nearly

impossible with light microscopy. This fact makes it difficult to validate

the here newly introduced method with existing methods. However,

applying light microscopy, the influence of the freeze‐drying process hasbeen evaluated. As shown in the Figures S1–S3, the freeze‐drying does

not appear to significantly modify either the size of the pellets or hyphal

thickness. A limitation of the new method is the high costs of µCT

measurements. In addition, three‐dimensional image analysis to obtain

morphological properties follows an elaborate workflow that requires

special computational expertize. As any other image analysis technique,

the here‐described three‐dimensional one has potential sources of

errors/inaccuracies, such as the selection of the gray value threshold

and the selection of the two parameters of the postprocessing steps.

Compared with other methods, such as microscopy and flow cytometry,

the sample number is low and the measurement rather time‐consuming.

µCTs have also lower voxel resolutions compared with pixels of

microscopic approaches.

5 | CONCLUSIONS

The present study describes a new method to determine the

morphological properties of the pellets of filamentous fungi. Freeze‐dried fungal pellets were analyzed using µCT measurements and three‐dimensional image analysis. µCT produces three‐dimensional images,

which is why the inner part of the fungal pellet can be studied along

with the outer part. To our knowledge, this is the first time that total

hyphal length, total tip number, total branch number, and HGU of entire

pellets can be determined with a single technique. Morphological

properties, such as porosity and average diameter of the hyphae, can be

studied in higher detail than ever before by using our method. By

elucidating the spatial morphological distribution, multiple hypotheses

regarding the morphological development of fungal pellets can be

formulated. Summarizing, compared with established methods, the new

method has significant advantages in analyzing the morphology of entire

pellets, including the hyphal network with the location of hyphal

material, tips, and branches. Main disadvantages are the low sample

number and high costs of the new method.

ACKNOWLEDGMENTS

The authors thank the Deutsche Forschungsgemeinschaft (DFG)

for the financial support for this work (BR 2035/11‐1 and ME

2041/5‐1) within the SPP 1934 DiSPBiotech. This work made use

of equipment that was funded by the Deutsche Forschungsge-

meinschaft (DFG INST 95/1111‐1). We also wish to thank Andrea

Pape for assistance with the preparation of pellets and Johann

Landauer for assistance with the microscope images. Strain

P. chrysogenum MUM 17.85 was provided by Prof. Dr. Armando

Venancio, Micoteca da Universidade do Minho, Braga, Portugal.

CONFLICT OF INTERESTS

The authors declare that they have no conflict of interests.

ORCID

Stefan Schmideder http://orcid.org/0000-0003-4328-9724

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SUPPORTING INFORMATION

Additional supporting information may be found online in the

Supporting Information section at the end of the article.

How to cite this article: Schmideder S, BarthelL, Friedrich T,

et al. An X‐ray microtomography‐based method for detailed

analysis of the three‐dimensional morphology of fungal

pellets. Biotechnology and Bioengineering. 2019;1–11.

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Supplementary Materials for Paper I: AnX-ray microtomography-based method fordetailed analysis of the three-dimensionalmorphology of fungal pellets

Figure S1: Light microscope images of A. niger pellets after 48 h fermentation: theupper row shows the “wet” states of pellets, whereas the lower row shows the freeze-dried states; Columns contain microscope images of the same pellet for the two states“wet” and freeze-dried.

33

Figure S2: Light microscope images of P. chrysogenum pellets after 48 h fermentation:the upper row shows the “wet” states of pellets, whereas the lower row shows the freeze-dried states; Columns contain microscope images of the same pellet for the two states“wet” and freeze-dried.

Figure S3: Light microscope images of P. chrysogenum pellets after 24 h fermentation:the upper row shows the “wet” states of pellets, whereas the lower row shows the freeze-dried states; Columns contain microscope images of the same pellet for the two states“wet” and freeze-dried.

34

Figure S4: Light microscope images of a P. chrysogenum pellet applying high resolutions:the upper row shows the “wet” state of the pellet, whereas the lower row shows thefreeze-dried state.

Figure S5: Light microscope images of outer regions of different P. chrysogenum pelletsapplying high resolutions: the upper row shows the “wet” state of pellets, whereas thelower row shows the freeze-dried state.

35

5.2 Paper II: From three-dimensional morphology to effective

diffusivity in filamentous fungal pellets (Schmideder et al.,

2019b)

Summary

The supply of pellets with nutrients and oxygen strongly influences their growth and pro-

ductivity. While the consumption of nutrients and oxygen is required for fungal metabolism,

their transport into pellets is mainly driven by diffusion. Although the dense hyphal network

is known to limit the diffusive mass transport of nutrients, oxygen, and secreted metabolites,

a well-founded correlation between structure and diffusivity does not exist. In this study,

we computed the effective diffusivities through a few hundred representative sub-volumes

of five Aspergillus niger pellets. The three-dimensional structures of the pellets were deter-

mined with µCT measurements and image analysis described in Paper I. Based on the diffu-

sion computations, we obtained a correlation between effective diffusivity and solid hyphal

fraction. This correlation is inspired by material laws for fibers, consistent with theoreti-

cal expectations, and shows an excellent fit to the investigated A. niger pellets. While the

correlation uncovered discrepancies with previously assumed laws for filamentous fungi, it

showed some similarities to laws for randomly oriented fibers. The findings of this study

enable the prediction of the diffusive transport of nutrients, oxygen, and secreted metabolites

in filamentous fungal pellets. This knowledge will improve morphological engineering of

pellets, and thus, contribute to increased productivities in bioprocesses. Restrictions of the

applied µCT system demanded the application of a fixed resolution for the measurements.

Further, pellets originated from a single experimental setup, which resulted in comparable

pellet-micromorphologies. However, both resolution and micromorphology can alter the dif-

fusivity. These limitations were overcome in Paper III.

Author contributions

Stefan Schmideder did the conception and design of the study and wrote the manuscript,

which was edited and approved by all authors. Heiko Briesen and Vera Meyer supervised the

study. Lars Barthel cultivated and freeze-dried fungal pellets. Stefan Schmideder and Henri

Müller conducted µCT measurements and image analysis. Stefan Schmideder set up mor-

phological simulations and diffusion computations. Stefan Schmideder and Heiko Briesen

interpreted the results. Stefan Schmideder and Lars Barthel proposed a workflow for biopro-

cess development.

36

© 2019 The Authors. Biotechnology and Bioengineering published by Wiley Periodicals, Inc.

Biotechnology and Bioengineering. 2019;1–12. wileyonlinelibrary.com/journal/bit | 1

Received: 5 July 2019 | Revised: 30 August 2019 | Accepted: 2 September 2019

DOI: 10.1002/bit.27166

AR T I C L E

Fromthree‐dimensionalmorphology toeffectivediffusivity infilamentous fungal pellets

Stefan Schmideder1 | Lars Barthel2 | Henri Müller1 | Vera Meyer2 |Heiko Briesen1

1Chair of Process Systems Engineering,

Technical University of Munich, Freising,

Germany

2Department of Applied and Molecular

Microbiology, Institute of Biotechnology,

Technische Universität Berlin, Berlin,

Germany

Correspondecne

Heiko Briesen, Technical University of

Munich, Chair of Process Systems

Engineering, 85354 Freising, Germany.

Email: [email protected]

Funding information

Deutsche Forschungsgemeinschaft,

Grant/Award Number: 198187031,

315305620,315384307

Abstract

Filamentous fungi are exploited as cell factories in biotechnology for the production of

proteins, organic acids, and natural products. Hereby, fungal macromorphologies adopted

during submerged cultivations in bioreactors strongly impact the productivity. In

particular, fungal pellets are known to limit the diffusivity of oxygen, substrates, and

products. To investigate the spatial distribution of substances inside fungal pellets, the

diffusive mass transport must be locally resolved. In this study, we present a new approach

to obtain the effective diffusivity in a fungal pellet based on its three‐dimensional

morphology. Freeze‐dried Aspergillus niger pellets were studied by X‐ray microcomputed

tomography, and the results were reconstructed to obtain three‐dimensional images. After

processing these images, representative cubes of the pellets were subjected to diffusion

computations. The effective diffusion factor and the tortuosity of each cube were

calculated using the software GeoDict. Afterwards, the effective diffusion factor was

correlated with the amount of hyphal material inside the cubes (hyphal fraction). The

obtained correlation between the effective diffusion factor and hyphal fraction shows a

large deviation from the correlations reported in the literature so far, giving new and more

accurate insights. This knowledge can be used for morphological optimization of

filamentous pellets to increase the yield of biotechnological processes.

K E YWORD S

Aspergillus niger, effective diffusion, filamentous fungal pellets, tortuosity, X‐ray microcomputed

tomography

1 | INTRODUCTION

Filamentous fungi are widely used cell factories for the production of a

variety of compounds such as enzymes, organic acids, or antibiotics

(Meyer, 2008). As just one example, plant‐biomass‐degrading enzymes

produced by filamentous fungi, have a global market value of € 4.7 billion

(Meyer et al., 2016). During submerged cultivation, filamentous fungi

adopt different macromorphological entities such as non‐aggregatedhyphae (disperse mycelia), loosely aggregated hyphal clumps, and densely

aggregated spherical structures (pellets; Pirt, 1966). This morphology is

influenced by the fungal species and cultivation parameters (Papagianni,

2004). Depending on the predominant morphology in a submerged

fungal culture, the substances produced by the organism can differ

significantly. As fungal growth and protein secretion are coupled

processes, it is for example known that the highest protein secretion

normally occurs during rapid hyphal growth, which takes place in

disperse mycelia and the outer layers of fungal pellets where nutrient

supply is not limited (Cairns, Zheng, Zheng, Sun, & Meyer, 2019). On the

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivatives License, which permits use and distribution in

any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.

37

other hand, the production of secondary metabolites peaks when the

producing organism shows an extremely low or zero growth (Brakhage,

2013). These conditions can be observed for example in the dense center

of fungal pellets, where the restricted diffusion of oxygen and nutrients

leads to limitations, thus inhibiting growth (Veiter, Rajamanickam, &

Herwig, 2018). This demonstrates that a detailed understanding of the

limitations and diffusion processes in fungal pellets is of crucial

importance for many biotechnological applications.

The effective diffusion coefficient is required to calculate the

diffusive mass transport. For component i in a porous medium, this

parameter can be expressed as (Becker, Wieser, Fell, & Steiner, 2011)

= ⋅D D k ,i i,eff ,bulk eff (1)

where Di,bulk is the diffusion coefficient of component i in the bulk

medium without geometrical hindrance and keff describes the reduction

of the free bulk diffusion Di, bulk to the effective diffusion

Di, eff and is solely dependent on the pore geometry and independent

of the diffusing substance i (Becker et al., 2011). Hereafter, keff is called

the effective diffusion factor. In the case of diffusion in filamentous

pellets, Di, bulk corresponds to the molecular diffusion coefficient of

components such as oxygen, glucose, or products in the fermentation

medium and is strongly dependent on the medium, diffusing substance,

and process conditions such as temperature. Temperature‐dependentbulk diffusion coefficients for glucose, oxygen, and several other

compounds in aqueous solutions can be estimated, for example, from

Yaws (2014). The geometrically caused reduction of the diffusion, keff,

can be expressed as (Epstein, 1989):

τ=ϵ

k ,eff 2(2)

where the porosity, ϵ, is defined as the ratio of volume of voids to the

total volume. The tortuosity, τ , is a geometrical parameter and can be

taken as the ratio of the average pore length to the length of the

porous medium along the major flow or diffusion axis. Thus, in

general it is > 1 (Epstein, 1989).

So far, no experimental or modeling approaches to exactly predict the

diffusive mass transport inside whole fungal pellets are available. Several

modeling approaches of filamentous microorganisms consider the

diffusive mass transport of oxygen and/or substrates like

glucose (Buschulte, 1992; Celler, Picioreanu, van Loosdrecht, & van

Wezel, 2012; Cui, Van der Lans, & Luyben, 1998; Lejeune &

Baron, 1997; Meyerhoff, Tiller, & Bellgardt, 1995; Table 1). They include

effective diffusion coefficients that are dependent on the molecular

TABLE 1 Applied correlations between effective diffusion coefficients (Di,eff), effective diffusion factor (keff), bulk diffusion coefficients(Di,bulk), porosity (ϵ), hyphal fraction ( = − ϵc 1h ), solid fraction (ϕ), and tortuosity (τ ) in the literature to model the diffusive transport

mechanisms

Eq. for keff in =D D ki i,eff ,bulk eff

Originstructure Diffusion direction Field Source

− c1 h – – Filamentous microorganisms Celler et al. (2012)

– – Filamentous microorganisms Cui et al. (1998) adopted from Van’t

Riet and Tramper (1991)

– – Filamentous microorganisms Buschulte (1992) adopted from Aris

(1975)

τ

( − )c1 h with τ = 2 – – Filamentous microorganisms Lejeune and Baron (1997)

−

+

c

c

2 2

2h

h

– – Filamentous microorganisms Meyerhoff et al. (1995) adopted from

Neale and Nader (1973)

(− )cexp 2.8 h – – Filamentous microorganisms Buschulte (1992) adopted from Vorlop

(1984)

ϕ

ϕ ϕϕ

ϕ

⎛

⎝

⎜⎜−

⎞

⎠

⎟⎟+ − −

−

1 2

1 0.013360.30583 4

1 1.40296 88

– Perpendicular to

fibers

Square array of parallel fibers Perrins et al. (1979)

τ

ϵ

2with τ = ( ( − ϵ))exp 1.16 12 Simulated Perpendicular to

fibers

Nonoverlapping parallel fibers Tomadakis and Sotirchos (1993),

Tomadakis and Robertson (2005)

τ

ϵ

2with τ ( )=

−

ϵ −2 1 0.33

0.33

0.707 Simulated Perpendicular to

fibers

Overlapping parallel fibers Tomadakis and Sotirchos (1991)

τ

ϵ

2with τ ( )=

−

ϵ −2 1 0.04

0.04

0.107 μCT Parallel to fibers Parallel carbon fibers Vignoles et al. (2007)

τ

ϵ

2with τ ( )=

−

ϵ −2 1 0.04

0.04

0.465 μCT Perpendicular to

fibers

Parallel carbon fibers Vignoles et al. (2007)

τ

ϵ

2with τ ( )=

−

ϵ −2 1 0.037

0.037

0.661 Simulated All directions Overlapping nonparallel fibers Tomadakis and Sotirchos (1991)

ϵ1.05 3 Simulated All directions Overlapping nonparallel fibers He et al. (2017)

2 | SCHMIDEDER ET AL.

38

diffusion coefficient, tortuosity, and porosity/hyphal fraction. Thereby, the

hyphal fraction, = − ϵc 1h , is defined as the ratio of the volume of

hyphae to the total volume. It is important to note that the modeling

approaches published so far (Buschulte, 1992; Celler et al., 2012; Cui

et al., 1998; Lejeune & Baron, 1997; Meyerhoff et al., 1995) either neglect

the tortuosity of the hyphal structure or assume a constant tortuosity for

different porosities. These simplifications may be caused by the absence

of information about the tortuosity. In the materials science of fibers,

correlations between the porosity and the effective diffusion factor for

bulk diffusion that include knowledge about the tortuosity have been

described. Perrins, McKenzie, and McPhedran (1979) derived an analytic

expression for ideal square arrays of parallel fibers, Tomadakis and

Sotirchos (1991) a correlation for random distributed overlapping parallel

fibers, Tomadakis and Sotirchos (1993) and Tomadakis and Robertson

(2005) a relation for random distributed nonoverlapping parallel fibers,

Tomadakis and Sotirchos (1991) and He, Guo, Li, Pan, andWang (2017) a

relation for 3D random distributed overlapping fibers, and Vignoles,

Coindreau, Ahmadi, and Bernard (2007) a correlation for parallel fibrous

carbon–carbon composite preforms (Table 1). The only published

experimental approach to predict the diffusive mass transport is based

on the measurement of oxygen concentrations using microelectrodes

inside fungal pellets (Hille, Neu, Hempel, & Horn, 2009; Wittier,

Baumgartl, Lübbers, & Schügerl, 1986). The researchers correlated the

mass transport of oxygen into the pellets with microscopic information

from cryo‐slices. However, the microscopy images of the cryo‐slicesmissed the three‐dimensional information of the hyphal network and

hyphae superimposed in the two‐dimensional projections. Therefore,

the appropriate correlation between pellet morphology and diffusion was

not possible in this experimental approach. We could recently overcome

the limitations of two‐dimensional image generation by performing X‐raymicrocomputed tomography (μCT) measurements on whole fungal pellets

(Schmideder et al., 2019). The investigated Aspergillus niger pellet showed

a very complex three‐dimensional structure. With a diameter of μ633 m,

the A. niger pellet had a hyphal length of 1.5m and 15,425 tips in total.

In materials science, μCT measurements and subsequent

mass‐transfer computations matured into a widely used method

to determine the effective diffusivity of porous/fibrous materials.

Exemplarily, Panerai et al. (2017), Becker et al. (2011), Coin-

dreau, Mulat, Germain, Lachaud, and Vignoles (2011), and

Foerst et al. (2019) investigated the effective diffusivity of

fibrous insulators, fuel cell media, carbon‐carbon composites, and

maltodextrin solutions, respectively. Thereby, μCT appeared as a

non‐destructive technique to measure three‐dimensional micro‐structures.

In this study, we computed the effective diffusivity of A. niger

pellets based on the micro‐structural characterization gained from

μCT measurements and subsequent image analysis. The newly

developed technique for fungal pellets combines the experimental

acquisition of three‐dimensional images with the locally resolved

calculation of the effective diffusion coefficient and tortuosity within

this structure for the first time. This results in an unprecedented

potential for the determination of diffusion processes inside fungal

pellets.

2 | MATERIALS AND METHODS

2.1 | Preparation of pellets

The A. niger hyperbranching strain MF22.4, which has been shown to

be a better protein‐secretion strain than the wild‐type strain (due to

deletion of the racA gene; Fiedler, Barthel, Kubisch, Nai, & Meyer,

2018), was used in this study. Pellets were obtained by submerged

cultivation of MF22.4 for 48 hr and freeze‐drying following the

previously described protocol (Schmideder et al., 2019).

2.2 | X‐ray microcomputed tomography

To obtain three‐dimensional images of the freeze‐dried filamentous

pellets, μCT measurements were performed based on the method

reported by Schmideder et al. (2019). Two‐dimensional projections

from different angles were reconstructed to generate three‐dimen-

sional images with a custom‐designed software (Matrix Technologies,

Feldkirchen, Germany) that uses CERA (Siemens, Munich, Germany).

The image resolution was 1 μm (i.e., the edge length of the voxels was

1 μm), and to generate the beam, 60 kV and 25 μA were applied.

Depending on the size of the pellets, 1‐5 pellets can be measured

with one μCT‐measurement (3 hr including the time for image

reconstruction). An instant adhesive (UHU, Bühl, Germany) was used

to fix the freeze‐dried fungal pellets on top of a sample holder. In

contrast to the previous study (Schmideder et al., 2019), in this case,

the instant adhesive dried 5min before placing the pellets on top of

the holder. This procedure resulted in a smooth surface of the instant

adhesive, while it remained sticky enough to fix the pellets. The

smooth surface facilitated the segmentation of the instant adhesive

in the subsequent image processing.

2.3 | Image processing

Image processing aimed at differentiating between hyphal material

and background. The background included the instant adhesive used

for sample fixation, the air between the hyphae, and small impurities.

In general, image processing is leaned to the one reported in the

section “Preprocessing” by Schmideder et al. (2019)). The image

processing result for one pellet is exemplarily illustrated in Figure 1.

As the instant adhesive showed similar gray values as the pellets,

we did not implement an automated segmentation. Instead, the

instant adhesive at the bottom of the pellets was cropped manually

using the commercial software VGSTUDIO MAX (version 3.2,

Volume Graphics GmbH, Heidelberg, Germany) in a first processing

step. The further image processing steps were carried out auto-

matically using MATLAB (version 2018a, MathWorks, Natick, MA).

To differentiate between hyphae and air voxels, a threshold –

calculated by Otsu’s method (Otsu, 1979) – was applied on the gray

value images. Finally, small connected objects with a maximum size of

1,000 μm3 were deleted to eliminate objects that were not part of

the pellet. The processed three‐dimensional pellets were used for

further diffusion computations.

SCHMIDEDER ET AL. | 3

39

2.4 | Representative cubes for diffusioncomputations of A. niger pellets

To compute the spatially resolved effective diffusivity in fungal pellets,

we extracted representative cubic sub‐volumes of the processed

three‐dimensional images. The diffusive mass transport was computed,

as described in Section 2.6 using these cubes. The centers of the cubes

used for diffusion computations were selected along the main axis

originating from the calculated mass center of the A. niger pellets. The

distance between the centers of the cubes along the main axis was set

to 25 μm. In Figure 2, the distance between the cubes was increased

for the sake of clarity. To identify the influence of the cube‐sizeon the diffusion computations, the edge length of the cubes was varied

to 30, 50, 70, and 90 μm.

2.5 | Beam‐Pellet

A common assumption for the effective diffusion coefficient

of filamentous microorganisms is the direct proportionality

to the porosity ϵ (Buschulte, 1992; Celler et al., 2012; Cui

et al., 1998; Silva, Gutierrez, Dendooven, Hugo, & Ochoa‐Tapia,2001):

= ⋅ ϵD D .i i,eff ,bulk (3)

Thereby, the effective diffusion factor keff is assumed to be equal to

the porosity, and the tortuosity is neglected. To imitate a filamentous

spherical object, where the tortuosity can be nearly neglected, we

simulated a so‐called “Beam‐Pellet,” which was used to validate the

F IGURE 1 Processed three‐dimensional μCT image of an Aspergillus niger pellet. The images were rendered using VGSTUDIO MAX.

(a) Projection of the whole pellet. (b) Projection of a central slice with a depth of 25 μm [Color figure can be viewed at wileyonlinelibrary.com]

F IGURE 2 Processed three‐dimensional μCT image of the Aspergillus niger pellet of Figure 1 and cubes for the diffusion computations:(a) Transparent: projection of a whole pellet; red: exemplary cubes that were used for the diffusion computations. (b–e) Morphology of asingle cube from different viewing directions; the gray boundaries in (c–e) illustrate the boundaries parallel to the diffusion computation.

(b) Cube without illustration of boundaries for the diffusion computations. (c) Cube for diffusion in the x‐direction. (d) Cube for diffusion in they‐direction. (e) Cube for diffusion in the z‐direction [Color figure can be viewed at wileyonlinelibrary.com]

4 | SCHMIDEDER ET AL.

40

method of the diffusion computation and critically scrutinize the

tortuosity neglect in the literature.

The “Beam‐Pellet” (Figure 3) was built up from equally sized

filaments (in diameter and length) with their origin in the pellet

center and having a radial orientation. To guarantee a uniform

distribution of the filaments in space, their orientation was calculated

using the HEALPIx (hierarchical equal area iso‐latitude pixelization)

discretization (Gorski et al., 2005). In this way, 50,700 representa-

tive, equally distributed points were calculated on the pellet surface;

all of them were connected to the pellet center. Then, the connected

lines were dilated with MATLAB to obtain a “Beam‐Pellet” with a

defined diameter of the filaments. The diameter was chosen to be

3 μm, similar to the average hyphal diameter of A. niger (Colin,

Baigorí, & Pera, 2013; Nielsen, 1993; Schmideder et al., 2019). To

investigate the influence of the image resolution on the subsequent

diffusion computations, similar “Beam‐Pellets” with different resolu-

tions were simulated. Starting from a ”Beam‐Pellet” with a radius of

700 voxels and a dilation of one voxel, the resolution of the filaments

was increased. Thereby, the number of filaments was kept constant,

whereas the radius of the “Beam‐Pellet” was set to 1,167, 1,633,

2,567, and 3,500 voxels and the dilation was set to 2, 3, 5, and

7 voxels, respectively. Thus, the “Beam‐Pellets” only differed in the

scaling and the resolution of the filaments. The effective diffusivity of

the “Beam‐Pellet” was analyzed, as described in Section 2.6. This

analysis required cubes that represent the whole pellet. Similar to the

case of the A. niger pellets, cubes located along the main axes were

chosen to investigate the effective diffusivity (Figure 3). Identical to

the final analysis of the A. niger pellets, the cube‐edge length was set

to 50 μm, and the cubes were selected along the main axis. Thus, the

cube edge length was 50 voxels for the “Beam‐Pellet” with a radius of

700 voxels and a dilation of one voxel. To guarantee that the same

structure (50 μm× 50 μm× 50 μm) was analyzed for higher

resolutions, we increased the cube edge length to 83, 117, 183,

and 250 voxels, respectively. In Figure 4, the same representative

cube is shown for different resolutions.

2.6 | Computation of the effective diffusivity

To compute the effective diffusion factor and tortuosity of

filamentous structures (Equation (2)), the module DiffuDict of the

commercial software GeoDict (Becker et al., 2011; Velichko,

Wiegmann, & Mücklich, 2009; Wiegmann & Zemitis, 2006;

Math2Market Gmbh, Kaiserslautern, Germany) was used. As

DiffuDict allows for the voxel‐based solution of transport equa-

tions, the processed three‐dimensional image data of the μCT

measurements as well as the simulated “Beam‐Pellet,” could be

used for the diffusion computations. DiffuDict requires cubic

domains for the diffusion computations, and therefore, cubic

sub‐volumes of the filamentous pellets were extracted from the

three‐dimensional images for further analysis. The selections of

representative sub‐volumes are described in Sections 2.4 and

2.5 for A. niger pellets and the “Beam‐Pellet,” respectively.

Conceptually, as shown in Figures 2c–e and 3c–e, the diffusion

computations in DiffuDict were executed in one of the three main

axes for each computation. As the representative cubes were chosen

along the main axes, we were able to apply three computations on

each cube and could thus analyze the effective diffusivity of each

cube in the radial and in two tangential directions. The computa-

tional effort to obtain the diffusivity of one cube in the three

directions was about 1 min for cubes with 50 × 50 × 50 voxels with

an Intel Xeon E5‐1660 CPU (3.7 GHz). The details of the computa-

tions are described in the following.

F IGURE 3 Simulated “Beam‐Pellet” and cubes for diffusion computations: (a) Transparent: projection of the whole pellet; red: exemplarycubes that were used for the diffusion computations. (b–e) Morphology of a single cube from different viewing directions; the gray boundaries

in (c–e) illustrate the boundaries parallel to the diffusion computation. (b) Cube without illustration of boundaries for the diffusioncomputations. (c) Cube for diffusion in the x‐direction. (d) Cube for diffusion in the y‐direction. (e) Cube for diffusion in the z‐direction [Colorfigure can be viewed at wileyonlinelibrary.com]

SCHMIDEDER ET AL. | 5

41

We computed the diffusion in the space/liquid between the

hyphae (porous medium). The predominant diffusion regime in

liquids is bulk diffusion (Becker et al., 2011; Panerai et al., 2017),

that is, mass transport is mainly driven by collisions between fluid

molecules. In our approach, we neglected surface effects on the

solid–liquid interface that could influence diffusion. One possible

effect could be surface diffusion, that is molecules can diffuse on

the surface of pores. This phenomenon is known to be an

important transport mechanism in reversed‐phase liquid chroma-

tography. However, predictions are difficult and depend on the

temperature, surface concentration, and surface chemistry

(Medveď & Černỳ, 2011; Miyabe & Guiochon, 2010). Electrical

double‐layers on solid–liquid interfaces could change the diffusiv-

ity through porous media, especially the diffusivity of ions (Gabitto

& Tsouris, 2017). In the present study we assumed pure bulk

diffusion. In the case of pure bulk diffusion, the diffusion in the

pores can be modeled by the Laplace equation, with Neumann

boundary conditions on the pores‐to‐solids boundaries and a

concentration drop of the diffusing component in the diffusion

direction (Becker et al., 2011). Thus, we applied bulk diffusion in

DiffuDict and applied a concentration drop of the diffusing

component between the inlet and outlet. To avoid a bias in the

diffusion computations, we chose Dirichlet boundary conditions on

the in‐ and outlet and symmetric boundary conditions on the other

four faces. Computing the total diffusion flux through the porous

structures and applying Fick’s law, DiffuDict calculates the

effective diffusion factor (Becker et al., 2011; Wiegmann &

Zemitis, 2006). According to Equation (2), the tortuosity can be

calculated from the porosity and the effective diffusion factor.

Therefore, both the effective diffusion factor and the tortuosity

were calculated for each representative sub‐volume of the

filamentous pellets.

3 | RESULTS AND DISCUSSION

3.1 | Effective diffusivity of the “Beam‐Pellet”

The “Beam‐Pellet” introduced in Section 2.5 (Figure 3) imitates a

hypothetical filamentous pellet that grew only in the radial

direction and is similar but not identical to parallel fibers. We

compared the diffusion behavior of the “Beam‐Pellet” with

literature correlations for the diffusion through parallel fibers

to validate the diffusion computations. Additionally, we

critically scrutinized the literature assumption that = ϵkeff

(Buschulte, 1992; Celler et al., 2012; Silva et al., 2001; Van’t

Riet & Tramper, 1991), where the tortuosity is neglected and the

effective diffusion factor is assumed to be only dependent on the

porosity.

F IGURE 4 Same representative cube of

“Beam‐Pellets” with different resolutions:(a) Three voxels per filament (dilation 1).(b) Five voxels per filament (dilation 2).

(c) Seven voxels per filament (dilation 3).(d) 15 voxels per filament (dilation 7)[Color figure can be viewed at

wileyonlinelibrary.com]

6 | SCHMIDEDER ET AL.

42

The results of the diffusion computations on the “Beam‐Pellet”are shown in Figure 5 for the hyphal fraction range 0.05–0.4. A

hyphal fraction of 0.4 was the maximum value for the A. niger pellets

investigated in this study. Figure 5a shows the relation between the

hyphal fraction of cubic sub‐volumes and their corresponding

effective diffusion factor. In the radial diffusion direction, the

effective diffusion factor decreased almost linearly with increasing

hyphal fractions. The radial effective diffusion factors showed a

similar behavior as that of the often applied assumption for

filamentous microorganisms: = ϵkeff (Buschulte, 1992; Celler et al.,

2012; Silva et al., 2001; Van’t Riet & Tramper, 1991). This formula is

the prediction of the “law of mixtures” for the flow along parallel

fibers (Tomadakis & Robertson, 2005). In the tangential directions,

the effective diffusion factors were much smaller than their radial

counterparts – and the slope was by no means in the order of minus

one. Figure 5b shows the tortuosities for the radial and tangential

diffusions, and it can be seen that they increase with increasing

hyphal fractions. As expected, the tortuosities in the tangential

diffusion direction were much higher than their radial counterparts.

To investigate the influence of the image resolution on the

diffusion computations, we simulated “Beam‐Pellets” with different

resolutions (Section 2.5). With increasing resolutions, the effective

diffusion factor increased and the tortuosity decreased, which

was probably caused by the increased circularity of the filaments

(Figure 4). As shown in Figure 3 and 4, representative cubes of the

“Beam‐Pellets” closely resemble parallel nonoverlapping fibers.

Literature correlations for bulk diffusion through parallel fibers

(Perrins et al., 1979; Tomadakis & Sotirchos, 1991, 1993; Tomadakis

& Robertson, 2005) suggest, that the applied diffusion computations

underestimate the diffusivity in the case of low resolutions. With

increased resolutions, the computed diffusion results approach the

literature correlations. However, it has to be mentioned that the

literature correlations are for a square array of parallel fibers

(Perrins et al., 1979), parallel random distributed overlapping fibers

(Tomadakis & Sotirchos, 1991), and random distributed nonoverlap-

ping fibers (Tomadakis & Robertson, 2005; Tomadakis & Sotirchos,

1993) and thus similar but not identical to our “Beam‐Pellets.”In contrast to the tangential diffusion paths, the radial paths of the

“Beam‐Pellet” were not winding (Figure 3). In theory, increased path

lengths result in an increased tortuosity and a decreased effective

diffusion factor (Epstein, 1989). This behavior could be observed for the

“Beam‐Pellet” in the radial and tangential diffusion directions as well.

The small difference between the computed radial effective diffusion

factors/tortuosities and the “law of mixtures” for the flow along parallel

fibers (Tomadakis & Robertson, 2005) = ϵkeff was evoked by the radial

direction of the filaments of the “Beam‐Pellet.” Thus, the filaments were

not completely parallel to each other. Further investigations with

simulated perfectly parallel filaments resulted in = ϵkeff and a constant

tortuosity of one (data now shown).

To sum up, the diffusion behavior of the “Beam‐Pellet” was

consistent with the diffusion theory described by Epstein (1989) and

could be used to verify the applied diffusion computations. The

comparison to literature correlations about the diffusivity of parallel

fibers suggests that our diffusion computations of fibers with a low

image resolution tend to underestimate the diffusivity, whereas high

resolutions approach the literature correlations. The radial diffusion

behavior of the “Beam‐Pellet” illustrated the often applied literature

assumption for filamentous microorganisms: = ϵkeff (Buschulte, 1992;

Celler et al., 2012; Silva et al., 2001; Van’t Riet & Tramper, 1991).

However, the morphology of the idealized “Beam‐Pellet” (Figure 3) was

very different from the μCT data of A. niger pellets (Figure 2). Thus, the

actual correlation between the effective diffusivity and the hyphal

fraction of A. niger pellets was investigated in further detail.

3.2 | Effective diffusivity of A. niger pellets

Contrary to the “Beam‐Pellet” (Figure 3), in the case of the A. niger

pellets, the voids, that is, the spaces between the hyphae (Figure 2),

(a) (b)

F IGURE 5 Diffusion computations of “Beam‐Pellets” in the radial and tangential directions and comparison to existing literature correlations forparallel fibers (Table 1). The “Beam‐Pellets” differ in the fiber‐diameter in voxels, whereas the diameter in μm stayed constant (Figure 4). Each data pointresults from a single diffusion computation of a cubic sub‐volume with a cube‐edge length of 50 μm. Crosses and circles correspond to computed

diffusion properties in the radial and tangential directions, respectively. The black lines represent literature correlations. The hyphal fraction correspondsto the ratio of the volume of hyphae to the total volume in the cubic sub‐volumes [Color figure can be viewed at wileyonlinelibrary.com]

SCHMIDEDER ET AL. | 7

43

are strongly winded. According to Epstein (1989) that should result

in an increased tortuosity, and therefore, in a decreased effective

diffusivity. The tortuosity and effective diffusion factors of five A.

niger pellets are investigated in this section. The diameters of the

pellets were between 410 and 570 μm.

To investigate the influence of the size of the cubic sub‐volumes

on the diffusion computations, the edge length of the cubes was

varied. Figure 6a shows the relation between the effective diffusion

factor and the hyphal fraction for different cube sizes. The data

include the diffusion computations of the five investigated A. niger

pellets in the radial direction for cube‐edge lengths of 30, 50, 70, and

90 μm. Generally, the effective diffusion factors for different cube‐edge lengths showed similar behavior. When no hyphal material is

present, that is, when the hyphal fraction is zero, the effective

diffusion factor is one, and thus, the diffusion is not geometrically

hindered. With increasing hyphal fraction, the effective diffusion

factor decreases. The applied cube‐edge lengths did not have a high

impact on the diffusion results. Thus, a cube‐edge length of 50 μm

was applied for further computations in this study. Figure 6b) shows

the effective diffusion factors of the five A. niger pellets studied

herein for a cube‐edge length of 50 μm. It can be seen that the values

for the different pellets varied only slightly. As five pellets were

investigated, this very subtle scattering of the data points implies

that the method is quite reproducible when applied to different

pellets obtained from the same cultivation sample.

Figure 7 shows the results of the diffusion computations for the

five studied A. niger pellets in the radial and tangential directions for

a cube‐edge length of 50 μm. Figure 7a shows that the computed

effective diffusion factors of the A. niger pellets were much smaller

than the values expected from the literature assumption = ϵkeff , and

therefore, also much smaller than the values obtained for the

investigated “Beam‐Pellet.” A slight anisotropy was observed when

comparing the radial and tangential diffusion directions because the

effective diffusion factors in the radial direction were slightly higher

(a) (b)

F IGURE 6 Correlations between the radial effective diffusion factor and hyphal fraction (ratio of the volume of hyphae to the total volume) for fiveAspergillus niger pellets. Each data point results from a single diffusion computation of a cubic sub‐volume: (a) Diffusion computations with different cubesizes. (b) The cube‐edge length was 50 μm; each color represents the investigated cubes of one pellet [Color figure can be viewed at

wileyonlinelibrary.com]

(a) (b)

F IGURE 7 Diffusion computations of five Aspergillus niger pellets in the radial and tangential directions. Each data point results from a singlediffusion computation of a cubic sub‐volume with a cube‐edge length of 50 μm; keff is the effective diffusion factor and ϵ is the porosity: (a) The

blue and green data points correspond to effective diffusion factors in the radial and tangential directions, respectively; the black linerepresents the literature assumption = ϵkeff . (b) The blue and green data points represent the tortuosities in the radial and tangential

directions, respectively [Color figure can be viewed at wileyonlinelibrary.com]

8 | SCHMIDEDER ET AL.

44

than their counterparts in the tangential direction. In the absence of

hyphal material, that is, when the hyphal fraction is zero, the

tortuosity is one (Figure 7b). With increasing hyphal fraction, the

tortuosity increases as well. Again, a slight difference was observed

between the radial and tangential diffusion directions, with the radial

diffusion computations resulting in lower tortuosities than their

tangential counterparts. According to Equation (2), the lower

tortuosities explain the higher effective diffusion factors in the radial

direction. In the model assumption = − + = ϵk c 1eff h , the tortuosity

is assumed to be constantly one. This simplification explains

the differences between our computed effective diffusion factors

for the A. niger pellets and the values expected from the literature

(Figure 7a) as well as those reported for the “Beam‐Pellet” in the

previous section.

The local hyphal fraction range of the five investigated A. niger

pellets was 0–0.4. To the best of our knowledge, there are no

reports in the literature, in which the hyphal fraction of filamentous

pellets is higher than the maximum hyphal fraction measured in this

study, for example, Cui, Van der Lans, and Luyben (1997, 1998)

reported average hyphal fractions between 0.07 and 0.30 for whole

Aspergillus awamori pellets. Thus, the hyphal fraction ranges of the

investigated A. niger pellets could already be representative for

realistic pellets.

3.3 | Correlation between effective diffusivity andhyphal fraction

The diffusion computations of the five investigated A. niger pellets

(Section 3.2) are compared to literature assumptions (Table 1) for the

correlation between the effective diffusion factor (keff) and the

hyphal fraction (ch)/solid fraction/porosity (ϵ = − c1 h) of filamentous

microorganisms (Figure 8a) and fibers (Figure 8b). As the diffusion of

spherical pellets should be driven mainly by radial diffusion, we have

investigated it herein. Additionally, a new modeling approach was

introduced to correlate the effective diffusion factor and the hyphal

fraction.

The computed diffusion factors differed strongly from the

assumption = ϵkeff , which has been used for simulation/modeling

studies of filamentous microorganisms by Celler et al. (2012),

Buschulte (1992), and Silva et al. (2001). In fact, the computed

effective diffusion factors were far below the expected values. In

those previous models, the effective diffusion factor was assumed to

be only dependent on the porosity of the material, while neglecting

the tortuosity. Thus, the difference between our computed effective

diffusion factors and previous assumptions (Buschulte, 1992; Celler

et al., 2012; Silva et al., 2001) was not surprising. The second linear

literature assumption for filamentous microorganisms was = ϵ/k 2eff

(Lejeune & Baron, 1997). In their work, Lejeune and Baron (1997)

considered the tortuosity to be consistently 2, without explaining

that assumption. As shown, their model differed strongly from the

computed data. Their model would result in a geometrically hindered

diffusion for a hyphal fraction of zero. Thus, especially for low hyphal

fractions, that assumption seems to be untenable. In their growth

modeling approach for filamentous microorganisms, Meyerhoff et al.

(1995) applied a nonlinear correlation between the effective

diffusion factor and the hyphal fraction: = ( − )/( + )k c c2 2eff h h . This

approach seemed to approximate our computed data better than the

two previous model assumptions from the literature. Additionally,

the effective diffusion factor is 1 and 0 for hyphal fractions of 0 and

1, respectively. In theory, these conditions should be fulfilled.

However, the model seemed to overestimate the effective diffusion

factors. Besides the assumption = ϵkeff , Buschulte (1992) deduced a

second model for filamentous microorganisms: = −k e ceff

2.8 h. In

comparison with the other literature assumptions for filamentous

microorganisms, this approach fitted our computed data best.

However, in the hyphal fraction range of 0–0.4, the model seemed

to underestimate the computed data. Additionally, for a hyphal

fraction of 1, the model would result in an effective diffusion factor of

(a) (b)

F IGURE 8 Correlations between hyphal fraction (ch)/solid fraction/porosity (ϵ = − c1 h) and effective diffusion factor (keff). The blue datapoints correspond to the computed effective diffusion factors of five Aspergillus niger pellets in the radial direction, with the cube‐edge length forthe diffusion calculations being 50 μm. The solid bold blue line shows the new correlation between the hyphal fraction and the effective

diffusion factor; the black lines represent existing correlations in the literature (Table 1) for (a) filamentous microorganisms and (b) 3D randomdistributed overlapping fibers [Color figure can be viewed at wileyonlinelibrary.com]

SCHMIDEDER ET AL. | 9

45

0.06. In theory, for a hyphal fraction of 1, the effective diffusion

factor has to be 0 (Epstein, 1989).

The correlations for 3D random distributed overlapping fibers

(Figure 8b) fitted our data better than the correlations existing for

filamentous microorganisms. Our data fall in between the correlation

of Tomadakis and Sotirchos (1991) and He et al. (2017). In both

studies, the computation of the effective diffusivity was well

validated for other structures like parallel fibers. However, they

differ significantly. Tomadakis and Sotirchos (1991) applied a

modification of Archie’s law (Archie, 1942) to correlate the tortuosity

factor τ α= (( − ϵ )/(ϵ − ϵ ))12p p , with the percolation porosity

ϵ = 0.037p and α = .661. It has to be mentioned that the modification

of Archie’s law also fitted well for Vignoles et al. (2007) for bulk

diffusion of μCT‐generated images of parallel fibrous carbon‐carboncomposite preforms. The percolation porosity was ϵ = 0.04p and

α α= ∕ =0.107 0.465 for diffusion parallel/perpendicular to the

fibers, respectively. According to Nam and Kaviany (2003), the

effective diffusivity of isotropic structures is often estimated using a

power function of porosity. Thus, He et al. (2017) fitted their

diffusion results of 3D random distributed overlapping fibers and

found α= ϵk neff , with α = 1.05 and =n 3.

To overcome the limitations and/or inaccuracies in the correla-

tions between the effective diffusion factor and hyphal fraction for

filamentous microorganisms and to obtain a relation with only one

fitting parameter, we propose a new correlation:

= ( − )k c1 ,aeff h (4)

where a is the only fitting parameter. This rather simple expression

guarantees theory‐consistent effective diffusion factors of 1 and 0 at

hyphal fractions of 0 and 1, respectively, and provides an excellent fit

to our data. Minimizing the error squares, = ±a 2.02 0.02 (with 95%

confidence bounds):

= ( − ) ±k c1 .eff h2.02 0.02 (5)

In conclusion, the literature assumptions for modeling diffusion in

filamentous pellets failed to fit our computed results, whereas

correlations for fibers in material science fitted our data better. Thus,

we set up a nonlinear equation (5) approach with only one fitting

parameter, which is a special case for the power function of porosity, for

α = 1 as well as for the modified Archie’s law, when ϵ = 0p . This

approach modeled the correlation between the effective diffusion factor

and the hyphal fraction for five investigated A. niger pellets quite well.

3.4 | Proposed workflow in bioprocessdevelopment

Depending on the product of interest, a saturation or a limitation

of substrates inside fungal pellets is pursued (Veiter et al., 2018).

To predict the spatial distribution of substrates inside pellets, the

effective diffusivity through the fibrous network has to be known

(Buschulte, 1992; Celler et al., 2012). Thus, our newly proposed

method to determine the effective diffusivity of filamentous fungal

pellets with μCT measurements and subsequent diffusion compu-

tations through the three‐dimensional morphology has consider-

able benefits for bioprocess development. We propose the

following idealized workflow to achieve an optimal/suitable pellet

morphology:

(1) Generate pellets through experiments or simulations

a) Cultivate different strains at different process conditions;

apply μCT measurements and subsequent image analysis of

pellets (Schmideder et al., 2019)

b) Simulate various three‐dimensional pellet‐networks with

algorithms similar to Celler et al. (2012); model calibration

could be carried out based on μCT measurements with

subsequent image analysis (Schmideder et al., 2019)

(2) Compute the correlation between the hyphal fraction and the

effective diffusivity for each existing and simulated pellet of

Step 1, as described in the present study

(3) Compute the proportion of substrate‐limited and substrate‐saturated regions of each pellet based on the consumption‐ anddiffusion‐terms of models such as Buschulte (1992)); apply

correlation of the hyphal fraction and effective diffusivity in

diffusion terms (this study; Step 2)

(4) Assemble data base of experimentally or simulatively generated

pellets including substrate‐supply and morphological features

(5) Select optimal/suitable pellet for the desired process from data base

(6) Realize optimal/suitable pellet in bioprocess, for example,

through the upscale of previous experiments (Step 1a), genetic

modifications, or process control

Obviously, some of these steps have to be investigated and

elaborated in much more detail to reach the proposed optimum

macromorphology through this workflow. However, we consider the

investigation of the effective diffusivity as an important step towards

morphological engineering. In our study, we investigated five pellets

of one process and the correlation between the effective diffusivity

and hyphal fraction scattered only slightly. Thus, we propose, that

our method is at least reproducible for a certain strain at certain

process conditions. If the observed correlation between the hyphal

fraction and the effective diffusivity is representative for the applied

A. niger strain in general, other fungal strains, and/or theoretically all

filamentous microorganisms should be the focus of future studies.

Thereby, as described, μCT measurements are suitable to detect the

three‐dimensional morphology used for diffusion computations.

However, other three‐dimensional methods such as confocal laser

scanning microscopy of pellets slices or even simulated pellets are

also conceivable to explore other strains and processes.

4 | CONCLUSIONS

The findings described in this manuscript unveil the actual relation

between the hyphal fraction (ch, i.e., the ratio between the volume of

10 | SCHMIDEDER ET AL.

46

hyphae and the total volume) and the effective diffusion factor (keff)

and tortuosity inside filamentous fungal pellets. They also uncover a

discrepancy with the assumptions made in the literature for

filamentous microorganisms so far. We propose a new correlation,

which is inspired by correlations for fibers, rather simple, consistent

with theoretical expectations, and shows an excellent fit to the

investigated A. niger pellets: keff=(1 − ch)2. Our μCT images resulted

in hyphae with a diameter of approximately five voxels. As indicated

in Section 3.1 and Figure 5, that might lead to a slight under-

estimation of the diffusivity. For future studies of fibers/filamentous

microorganisms, we recommend μCTs, that could resolve fibers/

hyphae to a diameter of approximate 11 voxels. Alternatively, a

correction factor could be calculated based on diffusion computa-

tions of simulated filamentous pellets. The method described in this

study is not limited to A. niger but can also be applied to a variety of

fungal species as well as to other organisms forming filamentous

structures. It is conceivable to use the described workflow not only

based on μCT data, but also on other three‐dimensional data such as

confocal laser scanning microscopy (CLSM) images of smaller

structures and pellet slices, or even simulated pellets. The computed

diffusion parameters, and thus the diffusion rates of substrates and

products inside fungal pellets, could in combination with a consump-

tion and production model, be applied to predict the actual metabolic

flux inside filamentous pellets. With this information, it would be

possible to propose an ideal fungal macromorphology for the

production of a certain substance, which could then be achieved by

genetic engineering and control of the process parameters during

fermentation.

ACKNOWLEDGMENTS

The authors want to thank Markus Betz and Christian Preischl for

preliminary studies on diffusion computations of filamentous

pellets and Clarissa Schulze for assistance with μCT measure-

ments. We also wish to thank Christoph Kirse and Michael Kuhn

for helpful discussions about diffusion mechanisms. This study

made use of equipment that was funded by the Deutsche

Forschungsgemeinschaft (DFG, German Research Founda-

tion)–198187031. The authors thank the Deutsche Forschungsge-

meinschaft for financial support for this study within the SPP 1934

DiSPBiotech–315384307 and 315305620.

CONFLICT OF INTERESTS

The authors declare that there is no conflict of interests.

ORCID

Stefan Schmideder http://orcid.org/0000-0003-4328-9724

Lars Barthel http://orcid.org/0000-0001-8951-5614

Henri Müller http://orcid.org/0000-0002-4831-0003

Vera Meyer http://orcid.org/0000-0002-2298-2258

Heiko Briesen http://orcid.org/0000-0001-7725-5907

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How to cite this article: Schmideder S, Barthel L, Müller H,

Meyer V, Briesen H. From three‐dimensional morphology to

effective diffusivity in filamentous fungal pellets.

Biotechnology and Bioengineering. 2019;1–12.

https://doi.org/10.1002/bit.27166

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5.3 Paper III: Universal law for diffusive mass transport

through mycelial networks (Schmideder et al., 2021)

Summary

In Paper II, we determined a law for the diffusivity through the hyphal network of one fungal

strain at defined process conditions. However, there are numerous fungal species capable of

forming pellets with strongly differing morphologies. To consider the broad morphological

range of filamentous fungi, we investigated the correlation between the effective diffusivity

and the structure of 66 µCT measured pellets from four fungal species (Aspergillus niger,

Penicillium chrysogenum, Rhizopus oryzae, and Rhizopus stolonifer) and 3125 Monte Carlo

simulated pellets. Simulated pellets allowed the variation of following morphological prop-

erties in ranges known to exist for filamentous microorganisms: branching frequency, hyphal

diameter, branch angle, maximum growth angle, and number of initial spores. As image

resolution is known to have an influence on diffusion computations, it was varied for simu-

lated structures. Thus, the simulated pellets overcame the limitations of Paper II, where the

results were based on one experimental set up and a fixed resolution for µCT measurements.

Based on diffusion computations through the mentioned simulated and measured pellets, we

determined a universal law, which unveiled that only one independent variable, the hyphal

fraction, affects the diffusivity. Because the simulations even considered the morphology

of filamentous bacteria, we propose that our law can be used to compute the diffusion of

molecules through any filamentous pellet. Concentrations of molecules inside pellets are af-

fected by metabolic rates and the transport through the dense network. As the transport can

now be calculated, the estimation of metabolic rates within pellets becomes feasible.

Author contributions

Stefan Schmideder did the conception and design of the study and wrote the manuscript,

which was edited and approved by all authors. Heiko Briesen and Vera Meyer supervised

the study. Lars Barthel and Ludwig Niessen cultivated filamentous fungi and prepared pellets

for µCT measurements. Henri Müller and Stefan Schmideder performed µCT measurements

of pellets. Stefan Schmideder, Henri Müller, and Tiaan Friedrich performed image analysis.

Stefan Schmideder and Tiaan Friedrich set up the code for morphological Monte Carlo sim-

ulations. Stefan Schmideder performed the diffusion computations and analyzed the results.

Stefan Schmideder, Henri Müller, Lars Barthel, and Heiko Briesen interpreted the results.

49

Biotechnology and Bioengineering. 2021;118:930–943.930 | wileyonlinelibrary.com/journal/bit

Received: 7 August 2020 | Revised: 13 October 2020 | Accepted: 31 October 2020

DOI: 10.1002/bit.27622

AR T I C L E

Universal law for diffusive mass transportthrough mycelial networks

Stefan Schmideder1 | Henri Müller1 | Lars Barthel2 | Tiaan Friedrich1 |

Ludwig Niessen3 | Vera Meyer2 | Heiko Briesen1

1School of Life Sciences Weihenstephan, Chair

of Process Systems Engineering, Technical

University of Munich, Freising, Germany

2Institute of Biotechnology, Faculty III Process

Sciences, Chair of Applied and Molecular

Microbiology, Technische Universität Berlin,

Berlin, Germany

3School of Life Sciences Weihenstephan,

Chair of Technical Microbiology, Technical

University of Munich, Freising, Germany

Correspondence

Heiko Briesen, Technical University of Munich,

Chair of Process Systems Engineering,

Gregor‐Mendel‐Str. 4, 85354 Freising,

Germany.

Email: [email protected]

Funding information

Deutsche Forschungsgemeinschaft,

Grant/Award Numbers: 198187031,

315305620, 315384307, 427889137

Abstract

Filamentous fungal cell factories play a pivotal role in biotechnology and circular

economy. Hyphal growth and macroscopic morphology are critical for product titers;

however, these are difficult to control and predict. Usually pellets, which are dense

networks of branched hyphae, are formed during industrial cultivations. They are

nutrient‐ and oxygen‐depleted in their core due to limited diffusive mass transport,

which compromises productivity of bioprocesses. Here, we demonstrate that a

generalized law for diffusive mass transport exists for filamentous fungal pellets.

Diffusion computations were conducted based on three‐dimensional X‐ray micro-

tomography measurements of 66 pellets originating from four industrially exploited

filamentous fungi and based on 3125 Monte Carlo simulated pellets. Our data show

that the diffusion hindrance factor follows a scaling law with respect to the solid

hyphal fraction. This law can be harnessed to predict diffusion of nutrients, oxygen,

and secreted metabolites in any filamentous pellets and will thus advance the ra-

tional design of pellet morphologies on genetic and process levels.

K E YWORD S

diffusive mass transport, filamentous fungal pellets, three‐dimensional morphological

measurements and simulations, X‐ray microcomputed tomography

1 | INTRODUCTION

Fungal biotechnology is key for the transition from a petroleum‐based economy into a bio‐based circular economy. A thinktank con-

sisting of leading European and American researchers and global

business leaders concluded that this biotech sector can help to

achieve 10 of the United Nations' 17 sustainable development goals

(Meyer et al., 2020). Filamentous fungi are the only microorganisms

that can fully degrade renewable lignocellulosic biomass and sus-

tainably transform it into food, feed, chemicals, fuels, commodities,

textiles, composite materials, antibiotics, and other drugs (Meyer

et al., 2020). Their ability to perform complex posttranslational

modifications (Wang et al., 2020), their greatly expanded natural

protein secretion apparatus (Ward, 2012), and the enormous po-

tential of the secondary metabolome to produce bioactive molecules

(Brakhage, 2013; Keller, 2019; Nielsen et al., 2017) make filamentous

fungi a favorable host for many applications (Wösten, 2019).

Filamentous fungi are usually cultivated under submerged con-

ditions in which their macromorphology varies from loose disperse

mycelia to dense hyphal networks called pellets (Papagianni, 2004;

Veiter et al., 2018). The evolution of these macromorphologies from

spores, germlings, and hyphae (collectively, structures of micro-

morphologies) is a multifactorial process and difficult to predict.

A recent review highlighted all known genetic, physiologic, medium,- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial License, which permits use, distribution and reproduction in any

medium, provided the original work is properly cited and is not used for commercial purposes.

© 2020 The Authors. Biotechnology and Bioengineering published by Wiley Periodicals LLC

50

and process parameters that impact the development of micro‐ andmacromorphologies of filamentous fungi, and it also discussed all

relevant advantages and disadvantages of macromorphologies with

regard to the production of fungal‐based bioprocesses (Cairns et al.,

2019). In brief, cultivations with disperse mycelia allow better

homogenous distribution of nutrients and oxygen but behave as non‐Newtonian fluids, whereas cultivations with pellets behave as

Newtonian fluids but suffer from nutrient and oxygen limitation in

the pellet cores. For Aspergillus niger and Penicillium chrysogenum

pellets, it was shown that oxygen was often only available in the

outer 200 μm (Hille et al., 2005; Wittier et al., 1986), whereas pellet

size could range from a millimeter to a centimeter in size. The areas

beyond this limit are likely hypoxic and do not sustain growth and/or

product formation.

Two factors determine the concentration of nutrients and pro-

ducts inside pellets (Celler et al., 2012; Cui et al., 1998; Lejeune &

Baron, 1997; Meyerhoff et al., 1995): the fungal metabolic rate and

the transport through the filamentous network. The transport is

mainly driven by diffusion, which is hindered by the dense hyphal

network (Hille et al., 2005). This transport limitation results in het-

erogeneity and substrate limitation inside pellets (Hille et al., 2009;

Veiter et al., 2020; Wittier et al., 1986; Zacchetti et al., 2018). The

following three prerequisites are necessary to compute the con-

centration profile of any nutrient or product within a pellet (Celler

et al., 2012; Cui et al., 1998; Lejeune & Baron, 1997; Meyerhoff et al.,

1995): (1) the micro‐ and macromorphologies of a pellet are known,

(2) the correlation between the morphology and the effective diffu-

sivity of the nutrient or product is known, and (3) the metabolic rate,

which is also dependent on (1), can be calculated. Notably, the me-

tabolic rate could be estimated if the first two prerequisites and the

concentration profile are known. We, therefore, recently harnessed

X‐ray microcomputed tomography (μCT) and three‐dimensional (3D)

image analysis to determine the location and number of tips, bran-

ches, and hyphal material within whole fungal pellets to meet the first

two requirements (Schmideder, Barthel, Friedrich, et al., 2019;

Schmideder, Barthel, Müller, et al., 2019). Mathematically, the con-

centration profile of any molecule i within the voids of a pellet could

be described by a diffusion reaction equation (Celler et al., 2012;

Meyerhoff et al., 1995), where the reaction term describes the con-

sumption or the production of the molecule. We focused on the

diffusion term, where the effective diffusion coefficient Di eff, of

component i determines the diffusivity and can be expressed as

(Becker et al., 2011):

D D k mi eff i bulk eff, , = ( )(1)

where m is the vector for morphological properties, and k meff ( ) is the

geometrical diffusion hindrance. The diffusion coefficient in the bulk

medium Di bulk, can be estimated from medium conditions (Yaws,

2009). Thus, k meff ( ), which is independent of the diffusing component

(Becker et al., 2011), is the only unknown variable to determine Di eff, .

It has to be mentioned that keff1− is similar to the formation factor,

which is often applied to describe the diffusivity, conductivity, or

permeability through porous media (Tomadakis & Robertson, 2005).

In our recent study (Schmideder, Barthel, Müller, et al., 2019), we

proposed the preliminary correlation k c1eff h2= ( − ) for one of the

main fungal cell factories, A. niger, where ch is the hyphal fraction

(equal to solid fraction).

In the current study, we investigated the correlation between

the effective diffusivity and the morphology of more than 60 μCT

measured pellets from four fungal cell factories (A. niger, P. chryso-

genum, Rhizopus oryzae, and R. stolonifer) and more than 3000 Monte

Carlo simulated pellets. We considered the diffusion through fila-

mentous networks with different resolutions because image resolu-

tion can influence computed material properties (Schmideder,

Barthel, Müller, et al., 2019; Velichko et al., 2009). Based on the

measurements and simulations, we propose here a generalized law

for the diffusion of nutrients, oxygen, and fungal metabolites through

hyphal networks. This law enables, for the first time, the estimation

of metabolic rates at any point within a pellet and forms the math-

ematical foundation for future targeted genetic and process en-

gineering strategies.

2 | MATERIALS AND METHODS

2.1 | Preparation of pellets

To obtain pellet structures of morphologically different strains of

industrially relevant fungal species, we cultivated the hyperbranching

A. niger MF22.4 (ΔracA) and its parental strain MF19.5 (Fiedler et al.,

2018; Kwon et al., 2011), P. chrysogenum MUM17.85 (indoor paint,

Micoteca da Universidade do Minho), R. stolonifer (isolated organ-

isms), and R. oryzae CBS 607.68 (unknown source). Sporangiospores

(Rhizopus spp.) and conidospores (A. niger and P. chrysogenum) of all

strains were obtained from agar plate cultures using standard pro-

cedures for filamentous fungi (Bennet & Lasure, 1991). Erlenmeyer

flasks were inoculated with the spores and cultivated for 24–48 h

until pellets became visible. Pellets were carefully removed by

pipetting, washed with sterile tap water, frozen while they were

floating in water, and subsequently freeze dried to preserve their

structure (Schmideder, Barthel, Friedrich, et al., 2019). For detailed

description of pellet preparation, we refer to Supplementary

Protocol 1.

2.2 | X‐ray microcomputed tomography

To obtain the 3D fibrous network of freeze dried pellets, μCT mea-

surements were performed based on the method reported previously

(Schmideder, Barthel, Friedrich, et al., 2019). Pellets were fixed on

top of a sample holder for image acquisition. Then, at least 2.000

two‐dimensional projections from different angles were acquired

using a μCT system (XCT‐1600HR; Matrix Technologies) and sub-

sequently reconstructed to 3D images with custom‐designed soft-

ware (Matrix Technologies) that is based on CERA (Siemens). Images

SCHMIDEDER ET AL. | 931

51

were taken with a voxel size of 1, 2, 3, and 4 μm, respectively. For

further information, we refer to Supplementary Protocol 2.

2.3 | Image processing

Image processing was applied on the 3D μCT‐images of the pellets,

based on the methods described previously (Schmideder, Barthel,

Friedrich, et al., 2019; Schmideder, Barthel, Müller, et al., 2019), to

differentiate between hyphal material and background. The back-

ground consisted of the material used for pellet fixation, air between

the hyphae, and small impurities.

First, the fixation material was cropped manually with the com-

mercial software VGSTUDIO MAX (version 3.2; Volume Graphics

GmbH) or automatically using MATLAB (version 2019b; MathWorks).

In the automatic segmentation, the gray level image was first binarised

by setting a gray value threshold, which was calculated with Otsu's

method (Otsu, 1979). After the binarisation, small connected objects

were removed, so that only the sample holder remained as a foreground

object in the binarised image. The complement of the binarized image

was calculated and multiplied with the original gray level image, re-

sulting in a gray level image without sample holder. Second, the pellets

were segmented from each other manually by drawing a region of in-

terest around each pellet with VGSTUDIO MAX or automatically using

MATLAB. Therefore, the gray level image without sample holder was

binarised by setting a gray value threshold, which was calculated with

Otsu's method (Otsu, 1979). The result was a binarised image with the

pellets as the foreground object. Furthermore, the binarised pellets

were dilated and a watershed segmentation (Meyer, 1994) was per-

formed. The segmented, labeled, and dilated pellet objects were read

out successively from the original gray level image with multiple pellets.

Finally, the resulting gray level images with only one single pellet were

cropped according to the pellet size.

To differentiate between the hyphae and the voids between the

hyphae on the cropped gray level images with single pellets, further

image processing steps were carried out automatically using

MATLAB (version 2019a). A. niger, R. stolonifer, and R. oryzae pellets

were binarised by setting a gray value threshold, which was calcu-

lated with Otsu's method (Otsu, 1979). However, for P. chrysogenum

pellets, this method was not sufficient. Therefore, the gray level va-

lues were clustered using Gaussian mixture modeling (Bishop, 2009;

McLachlan & Peel, 2000) with three classes. To reduce the compu-

tational effort, a random sample subset of 10% of the total voxel

count was drawn from the image and used for model creation. For

the sake of stability, the model was built seven times and the one

with the biggest log likelihood was chosen as the final model.

Afterwards, all voxels were classified against this model by calcu-

lating the largest posterior probability (Bishop, 2009). The three

classes represent the gray level values of the background, the noise,

and the hyphal material. All gray level values in the class of the

hyphal material were set to one, representing the foreground,

whereas the gray level values of the other two classes were set to

zero, representing the background in the binarised image.

After binarisation, connected objects smaller than or equal to

5000 μm3 for R. oryzae and R. stolonifer and 1000 μm³ for P. chryso-

genum, A. niger MF19.5, and A. niger MF22.4 were deleted, to elim-

inate small impurities between the hyphae.

Further diffusion computations were conducted with these final

processed 3D images of pellets.

2.4 | Diameter of hyphae

We used MATLAB (version 2019a) to determine the diameter of the

hyphae based on the maximum ball method (Silin & Patzek, 2006).

Therefore, we applied euclidean distance transform on the com-

plemented binarised 3D image with hyphae as foreground (MATLAB

function “bwdist”). As a result, the closest Euclidean distance of each

hyphal voxel to a nonhyphal voxel was stored in the 3D matrix D

(same dimension as the whole 3D image). Nonhyphal voxels were

assigned to zero. In addition, we applied ultimate erosion (MATLAB

function “bwulterode”) on the binarised 3D image, which resulted in

the 3D matrix E (same dimension as the whole 3D image), which

consisted of the regional maxima of the Euclidean distance transform

of the complement of the binarised image. To obtain the regional

hyphal diameters within whole pellets, the corresponding elements of

D and E were multiplied. The regional hyphal diameters were used to

calculate the arithmetic mean of the hyphal diameter.

2.5 | Morphological simulations

Our morphological simulations were based on stochastic growth

models for filamentous microorganisms (Celler et al., 2012; Yang

et al., 1992) and resulted in 3D images thereof. We implemented

the simulations in MATLAB (version 2019a). Video S1 visualizes

the growth process of an exemplary noncoagulative pellet from a

single spore. In our model, the following fundamental changes were

made compared with the model of Celler et al. (2012):

• New in our study: Spore aggregates can be used as initial condi-

tion; voxel‐based 3D image generation of morphological output

that makes the data comparable with μCT images.

• Neglected in our study: Cross wall‐formation; oxygen as a limiting

component for growth.

Our model can be divided into three sections: (1) spore aggregation,

(2) growth, and (3) generation of 3D structure (Figure 1). In the

following, the basics of the three sections are described.

We simulated spore aggregation based on the diffusion‐limited

aggregation (DLA) method (Witten & Sander, 1983; Figure 1, top).

DLA was initialized with a seed spore at the origin of a lattice. The

second spore started random walk from far away. The coordinate

was fixed if the second spore got in contact with the seed spore. If

the distance to the seed spore became too large, later contact would

be unlikely and the spore was rejected. The next spore started

932 | SCHMIDEDER ET AL.

52

random walk until it had contact or was too far from the spore ag-

gregate. This procedure was repeated until the desired number of

spores Nsp (Table S1) was reached.

Growth was based on the germination of spores, the extension of

tips, and the formation of branches (Figure 1, middle). The location of

spores served as input for the growth section, where they germi-

nated simultaneously in random orientations forming segments with

the length lgerm. Thereby, collisions of germlings with other germlings

or spores were prevented. After germination, the extension of tips

and the formation of branches started. These two phenomena re-

peated until the end of the cultivation. Exemplarily, a cultivation

period of t h48end = and a time step for calculations t h0.1∆ = would

result in 480 time steps. In each time step, the extension of each tip is

determined. Therefore, a growth angle gθ between 0° and the max-

imum growth angle is chosen randomly. The length of the new seg-

ment lsegment is the product of t∆ and the tip extension rate tα . The

growth angle and the length of the segment form a circle, whereon

the location of the new tip is calculated randomly (Figure 1). The new

segment is defined as the connection between the old and the new

tip. To prevent overlapping hyphae, possible collisions between the

new segment and other segments or spores are detected with

closest‐point computations (Ericson, 2010). If a collision is detected,

the new segment is rejected. However, the same tip is checked for

extension in the next calculation step. Similar to Celler et al. (2012),

F IGURE 1 Overview of the algorithm of morphological simulations [Color figure can be viewed at wileyonlinelibrary.com]

SCHMIDEDER ET AL. | 933

53

new branches could be formed in the subapical region of hyphae. The

subapical region had a length of lsubapical and started beginning from

the tip (Table S1). In each time step, one possible new branch point

(node between two segments, Figure 1) per subapical region was

chosen randomly. Before the new branch was generated at this

branch point, four conditions had to be fulfilled: (1) location in sub-

apical region, (2) no branches in the neighboring four nodes,

(3) current number of branches of the hyphae was lower than the

possible number of branches, and (4) no collision of new segment

with other segments or spores. The possible number of branches per

hyphae was calculated by dividing the length of the hyphae by the

minimum mean distance between two branches db min, (Table S1). If

conditions one through three were fulfilled, a possible new branch

was calculated. The branch angle bθ and the length of the segment

lsegment formed a circle, whereon the location of the tip of the new

branch was calculated randomly (Figure 1). Similar to the extension

of tips, the new segment was checked for collisions with other seg-

ments or spores (Ericson, 2010) and rejected if a collision was de-

tected. Finally, the growth section resulted in morphological

information, that is, the location and connection of nodes, hyphal

segments, and spores.

The morphological information of the growth section served as

input to generate voxel‐based 3D structures (Figure 1, bottom). To

scale the 3D images, the location of nodes (points between segments

or center of spores) was multiplied with the scaling factor fd

dscaleh vx

h

,= ,

where dh vx, and dh are the hyphal diameters in voxels and μm, re-

spectively. Varying dh vx, for the same morphological information

generated 3D images of pellets only differing in resolution. To obtain

skeletons of pellets, the connections between nodes were discretised

based on Bresenham's line algorithm (Bresenham, 1965). Finally, the

skeletonized images were dilated using a spherical structuring ele-

ment to obtain 3D images of pellets with the desired hyphal diameter

and resolution.

2.6 | Diffusion computations

We computed the continuum diffusion through the voxel‐basedstructures of filamentous pellets gained from both simulations and

processed μCT measurements. Similar to our previous study

(Schmideder, Barthel, Müller, et al., 2019), we calculated the diffusive

mass transport using the commercial software GeoDict (Becker et al.,

2011; Velichko et al., 2009; Math2Market Gmbh) that uses the ex-

plicit jump finite volume solver by Wiegmann and Zemitis (2006) for

diffusion computations. Depending on the size of the pellets, ap-

proximately 50–150 representative cubic sub‐volumes per pellet

were extracted using MATLAB (version 2019a) and further used for

diffusion computations (Video S2). An edge length sixfold the hyphal

diameter proved to be sufficient as representative elementary

volume (REV) of the extracted cubes to fit the parameter a in

k c1eff ha= ( − ) (Figure S1) and to investigate the porosity and dif-

fusivity (Figures S2 and S3). The cubes were selected along the three

main axes originating from the calculated mass center of the pellets.

We applied a diffusion computation in the radial direction of each

extracted cube, resulting in an effective diffusivity (keff ) in radial di-

rection, that is, the direction pointing to the mass centre of the pellet.

In addition, the hyphal fraction (ch) of the cubes, that is, the ratio of

volume of hyphae to the total volume, was analyzed. Similar to our

previous study (Schmideder, Barthel, Müller, et al., 2019), the diffu-

sion computations were conducted in the liquid between the hyphae,

the porous medium. Pure bulk diffusion was assumed, because it is

the predominant diffusion regime in liquids (Becker et al., 2011;

Panerai et al., 2017). In our study we neglected surface effects on the

solid‐liquid interface that could influence diffusion (Schmideder,

Barthel, Müller, et al., 2019). The diffusion was modeled by the

Laplace equation, with Neumann boundary conditions on the pores‐to‐solids boundaries, and a concentration drop of the diffusing

component in the diffusion direction (Becker et al., 2011). In addition,

we applied Dirichlet boundary conditions on the in‐ and outlet and

symmetric boundary conditions on the other four faces.

3 | RESULTS AND DISCUSSION

3.1 | Correlation of morphology and diffusive masstransport in µCT‐measured pellets

Because pellet morphology is, inter alia, strain dependent, we in-

vestigated five different strains from four fungal cell factories: P. chry-

sogenum (penicillin producer); A. niger (citric acid and enzyme producer,

with one isolate displaying wildtype morphology; strain MF19.5), and

one hyperbranching isolate (strain MF22.4; Fiedler et al., 2018));

R. stolonifer (fumaric acid); and R. oryzae (enzymes, tempeh). At least

three pellets per strain were analyzed by μCT, which allows non‐destructive 3D investigations of intact pellets (Schmideder, Barthel,

Friedrich, et al., 2019). The 3D morphology and an exemplary diffusion

computation through a R. stolonifer pellet are shown in Video S2.

Remarkably, pellet morphologies were highly diverse among the

strains (Figure 2). Equatorial slices of pellets showed that the dis-

tribution of hyphal material ranged from nearly spherically sym-

metric (R. oryzae, R. stolonifer, and A. niger) to a distribution far from

spherical symmetry (P. chrysogenum). The porosity within the pellets

also differed significantly. For example, R. stolonifer pellets had a

loose structure whereas A. niger pellets were much denser. In addi-

tion, the porosity varied from nearly homogeneous (A. niger MF22.4

and R. stolonifer) to strongly heterogeneous (R. oryzae and P. chryso-

genum). The mean hyphal diameter of P. chrysogenum, A. nigerMF19.5,

A. niger MF22.4, R. stolonifer, and R. oryzae was 4.3, 4.0, 4.3, 8.3, and

4.5 μm, respectively. Although the morphology of the investigated

strains varied strongly, the results of the diffusion computations

were surprisingly very similar (Figure 2, bottom row). The correlation

k c1eff ha= ( − ) (2)

between the effective diffusion factor (keff ) and the hyphal fraction

(ch, ratio of hyphal material inside the cubes) fitted well for all strains.

934 | SCHMIDEDER ET AL.

54

The correlation is known as Archie's law with a cementation para-

meter equal to a (Archie, 1942) and was already applied for one

A. niger strain in our previous study (Schmideder, Barthel, Müller,

et al., 2019). Including the 95% confidence interval, the exponent a

was 2.05 0.04± , 2.07 0.03± , 1.99 0.02± , 1.99 0.02± , and

1.99 0.04± for P. chrysogenum, A. niger MF19.5, A. niger MF22.4, R.

stolonifer, and R. oryzae, respectively.

The similarity of the diffusion laws raises the issue of a gen-

eralized law for filamentous fungi. However, as there are an esti-

mated six million fungal species on earth (Taylor et al., 2014), many of

them filamentous and capable of forming numerous different

morphologies (Cairns et al., 2019), our μCT‐based experimental ap-

proach is not target orientated to investigate a generalized law.

3.2 | Correlation of morphology and diffusive masstransport in simulated pellets

To determine a generalized law for the diffusivity through fungal

pellets that would be applicable to any filamentous fungus of interest,

we decided to follow an unbiased modeling approach. Using a Monte

Carlo growth model (Celler et al., 2012; see Section 2), we thus si-

mulated a huge variety of pellet morphologies and then exposed the

simulated pellets to diffusion computations (see Section 2 and

Video S2).

In the morphological simulations, both the coagulative and

noncoagulative fungal spore aggregation phenomena (Metz &

Kossen, 1977; Zhang & Zhang, 2016) were taken into account. In

brief, a coagulative pellet forms by aggregation of hundreds to

thousands of spores before they start to germinate, and a non-

coagulative pellet could form from the germination of a single

spore (Cairns et al., 2019). For the former case, we decided to

model the aggregation of spores by diffusion‐limited aggregation

(Witten & Sander, 1983; see Section 2). Figure 3 highlights that

the unbiased morphological simulations indeed enabled the de-

velopment of both coagulative and noncoagulative pellet types,

which reasonably matched the experimental data for the coagu-

lative A. niger MF19.5 and the noncoagulative R. stolonifer, re-

spectively. The growth process of a non‐coagulative pellet is

shown in Video S1.

F IGURE 2 Morphology and diffusivity of experimentally investigated pellets. Upper two rows: Exemplary projections of processedthree‐dimensional microcomputed tomography (μCT) images. Slices are from equatorial regions with a depth of 30 μm. Cubes are

50 × 50 × 50 μm. Bottom row: correlation between hyphal fraction (ch) and effective diffusion factor (keff ). Each blue data point corresponds toone cube applied for diffusion computations. The solid blue line is the correlation between the hyphal fraction and the effective diffusionfactor, resulting in the fitted exponent a in (Schmideder, Barthel, Müller, et al., 2019): k c1eff h

a= ( − ) . ± specifies the 95% confidence interval.μCT measurements were conducted with a voxel size of 1 μm (three Penicillium chrysogenum, three Aspergillus niger MF19.5, five

A. niger MF22.4, and three Rhizopus oryzae pellets) and 2 μm (11 R. stolonifer pellets). For each strain, at least 149 cubes were investigated.Scale bar: 100 μm [Color figure can be viewed at wileyonlinelibrary.com]

SCHMIDEDER ET AL. | 935

55

Pellet formation is not only dependent on coagulative and non-

coagulative spore aggregation type but also on the genetic make‐upof the species and process‐relevant parameters (Cairns et al., 2019).

To simulate a broad range of morphologically different pellets, our

simulation therefore considered high variation of five morphological

parameters (Figure 4): maximum growth angle, branch angle, hyphal

diameter, branch interval, and number of initial spores. For each of

these parameters, five values were estimated, resulting in 5 31255 =

morphologically different structures in total. In a recent study

(Lehmann et al., 2019), the investigation of 31 filamentous fungal

species resulted in mean branching angles between 26° and 86°, mean

internodal lengths (distance between two branches) between 40 and

453 μm, and mean hyphal diameters between 2.7 and 6.5 μm. How-

ever, the diameter of fungal hyphae has been reported to range from 2

to 10 μm (Meyer et al., 2020; Zacchetti et al., 2018). We decided to

also consider in the simulations the hyphal diameter of filamentous

bacteria (about 0.5–1 μm), as filamentous bacteria are morphologically

similar to filamentous fungi (Nielsen, 1996; Zacchetti et al., 2018), with

Streptomycetes as important cell factories for antibiotic production

(Nepal & Wang, 2019). In our simulations, the parameter branch angle

was set to 20°, 55°, 90°, 125°, or 160°, whereby angles larger than 90°

orient the branch towards the opposite direction of the leading

hyphae. The morphological parameter branch interval was defined as

the ratio between the internodal length and the hyphal diameter,

scaled with the hyphal diameter because large internodal lengths are

linked with large hyphal diameters (Lehmann et al., 2019). As

expected, simulations with large branch intervals produced disperse

mycelia instead of pellets. Thus, we set the maximum branch interval

F IGURE 3 Experimental and simulated coagulative and noncoagulative pellet formation. First and third rows show experimental data ofcoagulative pellet forming Aspergillus niger MF19.5 (Fiedler et al., 2018) and noncoagulative pellet forming Rhizopus stolonifer, respectively.

Second and fourth rows illustrate simulations of coagulative and noncoagulative pellet formation, respectively. First column shows spore(aggregates), second column germinated spore (aggregates), third column two‐dimensional (2D) projections of three‐dimensional (3D) pellets,and fourth column slices of pellets with a depth of 30 μm. Images of experimental spore aggregates were captured with light microscopy,whereas experimental pellets were measured with microcomputed tomography (μCT) to determine 3D images. Spore aggregation of coagulative

pellet formation was simulated with the diffusion‐limited aggregation method (Witten &amp; Sander, 1983) and 2048 spores. Pellet growth wassimulated with the Monte Carlo model described in Section 2. Scale bar: 100 μm

936 | SCHMIDEDER ET AL.

56

to 35. The maximum number of initial spores was set to 10,000 be-

cause coagulative pellets can result from hundreds or thousands of

agglomerated spores (Fontaine et al., 2010; Metz & Kossen, 1977).

Due to the lack of literature describing the growth angle of hyphae, we

varied the maximum growth angle within a range to consider straight

growing (0°) and strongly curved (48°) hyphae.

Our Monte Carlo simulations covered a broad morphological

range of filamentous fungal pellets, which we believe also includes

pellets reflecting macromorphologies from smaller filamentous

bacteria.

Because image resolution could influence computed properties

(Schmideder, Barthel, Müller, et al., 2019; Velichko et al., 2009), we

further investigated the influence of pellet resolution on their dif-

fusivity. In Figure 5a, an exemplary cube of a simulated pellet is

shown that differs only in resolution, that is, the number of voxels

that span a given hyphal diameter. In this figure, the image resolution

increases from top to bottom, and the hyphae appear more cylind-

rical. Notably, the a value in k c1eff ha= ( − ) decreases with increasing

resolution of three exemplary simulated pellets and converges to

a1.6 1.8< < , suggesting that the a value converges with increasing

resolution.

To investigate the influence of the image resolution of experi-

mentally determined pellets on their diffusivity, we thus conducted

μCT measurements with different resolutions. In particular, R. stolo-

nifer pellets were measured with a voxel size of 1, 2, 3, and 4 μm and

R. oryzae pellets with a voxel size of 1 and 2 μm. The decrease in the

voxel size led to an increased resolution. Similar to simulated pellets,

a in k c1eff ha= ( − ) decreased with increasing resolution (Figure 5b).

Note that (i) measurements with a voxel size of 1 μm in the case of

R. stolonifer, the organism with the highest hyphal diameter in this

study, result in hollow hyphae (Figure S4), which cannot be used for

diffusion computations and (ii) that low resolutions result in coarse

surfaces of the hyphae that do not reflect their smooth nature. Thus,

3D images of filamentous pellets are limited to a minimum and

maximum resolution for each organism, which strongly depends on

their hyphal diameters. We therefore propose the application of an

image resolution that represents hyphae with about four to six voxels

in diameter.

Tomadakis and Robertson (2005) summarized and extended

correlations between the morphology and the diffusivity, con-

ductivity, and permeability through fiber structures with different

orientations. The study was based on previous studies by Tomadakis

& Sotirchos, (1991, 1993, 1993, 1993). To validate our diffusion

computations and to identify an appropriate resolution for simulated

pellets, we compared the solution for randomly orientated over-

lapping straight fibers by Tomadakis and Sotirchos (1991) with our

computed diffusivity through such a morphology. We set up a si-

mulation with 1000 spores, a growth angle of 0°, and allowed colli-

sions (Figure 6a) to obtain randomly orientated overlapping straight

fibers. As shown in Figure 6b,c, our simulated structure was

F IGURE 4 Applied morphological parameters for simulations of filamentous structures. Five morphological parameters were applied:

maximum growth angle, branch angle, hyphal diameter, branch interval (ratio between the distance between two branches and the hyphaldiameter), and number of initial spores. Each of these parameters was varied to five values resulting in a total of 5 31255 = simulationsperformed with the Monte Carlo method described in Section 2

SCHMIDEDER ET AL. | 937

57

comparable to the structure used for the correlation

keff0.037

1 0.037

0.661ε

ε( )=−

−(Tomadakis & Sotirchos, 1991). With increasing

resolution, that is, with increasing voxels representing the hyphal

diameter, the computed diffusivities of the simulated structure ap-

proached the correlation of Tomadakis and Sotirchos (1991;

Figure 6d). Especially in the hyphal fraction range 0–0.4, our com-

puted diffusivities fit well with their correlation, suggesting that the

diffusion computations were accurate for high resolutions in the

hyphal fraction range 0–0.4. The range reflects the hyphal fraction of

both simulated and experimentally determined pellets (Figures 2

and 7, see next Section 3.3).

3.3 | Merging diffusive mass transport data fromsimulated and µCT measured pellets

We investigated the diffusive mass transport in filamentous fungal

mycelia through the correlation between the diffusivity and mor-

phology of 3125 simulated and 66 μCT analyzed pellets. We applied

an image resolution that represented simulated hyphae five voxels in

diameter to make the results of simulations and experiments com-

parable (Figure 7a). Because this resolution could underestimate the

diffusivity (Figure 6 and our previous study; Schmideder, Barthel,

Müller, et al., 2019), we also applied a resolution that represented

hyphae with 13 voxels in diameter (Figure 7b). We considered this

resolution as a compromise between accuracy and computational

effort of diffusion computations. Similar to experimentally de-

termined pellets, we used several cubes of each simulated structure

for diffusion computations.

Interestingly, pellet formation did not occur for all parameter

combinations. The combination of low spore numbers and rare

branches resulted in dispersed mycelia instead of pellets. Thus, we

marked loose structures with a mean hyphal fraction of the re-

spective cubes less than 0.05. As a result, the initial 3125 simulated

structures were reduced to 1280 and 1791 pelletised structures for

hyphae represented with 5 and 13 voxels, respectively (Figure 7). The

mean correlation factor a aσ± ( ) of all 3125 structures was

a 2.059 0.182= ± and a 1.757 0.150= ± for hyphae represented

with 5 and 13 voxels, respectively (Figure 7, top and bottom). For

pelletized structures, the mean was altered to a 2.063 0.044= ±

and a 1.753 0.035= ± , respectively. In Figure 7, pellets with unlikely

morphological parameters were marked, namely all pellets with

straight hyphae (maximum growth angle 0= °) or extreme branch

angles (branch angle 20= ° and branch angle 160= °). Thus, the

F IGURE 5 Relationship between image resolution and effective diffusivity. Image resolution is represented by the number of voxels thatspan a given hyphal diameter. Left: Identical exemplary cube of a simulated pellet that differs only in image resolution. Exemplarily, hyphae

are represented with 3, 7, and 11 voxels in diameter. Right: a value of experimentally determined pellets and three exemplary simulated pelletsfitted on a base of at least 37 cubes per pellet with k c1eff h

a= ( − ) , where keff is the effective diffusion factor, ch the hyphal fraction,and a the fitted correlation factor (Schmideder, Barthel, Müller, et al., 2019). Morphological simulations of pellets were performed with the

Monte Carlo method described in the Section 2. Rhizopus pellets were measured with microcomputed tomography (μCT) with a voxelsize of 1 μm (three R. oryzae pellets), 2 μm (21 R. oryzae and 11 R. stolonifer pellets), 3 μm (13 R. stolonifer pellets), and 4 μm(seven R. stolonifer pellets). Each data point of measured pellets was fitted on the base of cubes of the mentioned number of pellets.

Error bars specify the 95% confidence interval [Color figure can be viewed at wileyonlinelibrary.com]

938 | SCHMIDEDER ET AL.

58

number of pellets was reduced to 898 and 712, with a narrow

distribution of the correlation factor a 2.072 0.025= ± and

a 1.760 0.023= ± for hyphae represented with 5 and 13 voxels in

diameter, respectively. Pellets with unlikely morphological para-

meters explain the outliers for the correlation factor a. For the ex-

perimentally determined pellets of P. chrysogenum, A. niger MF19.5,

A. nigerMF22.4, R. stolonifer, and R. oryzae, a was 2.05, 2.07,1.99,1.99,

and 1.99 (Figure 2), respectively, and thus in the range of the simu-

lated pellets where the hyphae are represented with 5 voxels in

diameter (Figure 7, top). Applying the maximum ball method

(Section 2), this is a mean hyphal diameter of 4.5 voxels that lies in

the range of our experimental pellets (4.3, 4.0, 4.3, 4.2, and 4.5 voxels

for the different strains).

The results strongly indicate that the diffusion law k c1eff ha= ( − )

is applicable to fungal pellets with arbitrary morphology. In addition,

the only fitting parameter a lies in a narrow range while the resolution

of the images does not change. This implies that there is a

generalizable law for the diffusivity through fungal pellets with the

hyphal fraction ch as the only independent variable. Contrary to our

expectations, detailed morphological parameters such as growth

angles, branch angles, hyphal diameters, number of initial spores, and

branching frequency did not affect the diffusive hindrance. For all

3125 simulated pellets we applied image resolutions to represent the

hyphal diameter with 5 and 13 voxels, respectively. We were able to

show that low resolutions (Figure 7a) lead to an underestimation of

the diffusivity (Figure 6 and our previous study; Schmideder, Barthel,

Müller, et al., 2019). In addition, the results of three simulated pellets

with different image resolutions (Figure 5b) show that the a parameter

converges with increasing resolution for each pellet. Thus, we suggest

to use the law for high resolutions (the hyphal diameter is represented

with 13 voxels in diameter; Figure 7b) to calculate the diffusivity

through fungal pellets:

k c1eff h1.76= ( − )

(3)

F IGURE 6 Validation of diffusion computations. The solution for the effective diffusion factor keff through randomly orientated overlappingstraight fibers keff

0.037

1 0.037

0.661ε

ε( )=−

−by Tomadakis and Sotirchos (1991) was compared with the computed keff through similar simulated structures.

The porosity was 1 hyphalfractionε = − . We performed the morphological simulations with the Monte Carlo method described in the Methods

section. (a) Whole simulated structure. (b) Exemplary cube of simulated structure. For diffusion computations, 76 cubes were investigated for eachresolution. Resolution is represented by the number of voxels that spanned the given hyphal diameter. (c) Model structure applied for solution byTomadakis and Sotirchos (1991). (d) Solution by Tomadakis and Sotirchos (1991) (black line) and computed diffusivities through simulated structure.

Each data point corresponds to the diffusivity through one cube [Color figure can be viewed at wileyonlinelibrary.com]

SCHMIDEDER ET AL. | 939

59

where keff is the effective diffusion factor (keff1− is similar to the for-

mation factor) describing the geometrical diffusion hindrance

through a 3D structure, and ch is the hyphal fraction (similar to solid

fraction). As shown in Figure S5, our law is not very distinct from the

law of random orientated overlapping fibers by Tomadakis and So-

tirchos (1991). However, our correlation differs very strongly from

the correlation for random orientated overlapping fibers proposed by

He et al. (2017). For low porosities, the correlation of He et al. (2017)

proposes effective diffusion factors larger than 1, which is physically

unreasonable. It has to be mentioned that our law might slightly

underestimate the diffusivity through filamentous fungal networks,

because Figure 5 implies that the convergence might not be fully

developed for a resolution of 13 voxels. However, doubling the re-

solution increases the volume of pellets and cubes for diffusion

computations eightfold. The increase of the cube‐volumes would

result in excessive computational times (With a resolution of 13

voxels, the diffusion computations of all 3125 pellets last about 3

weeks with an Intel Xeon E5‐1660 CPU (3.7 GHz)). In addition, some

pellets could not be reconstructed with very high resolutions because

they would result in working memories larger than our available

128 GB. Thus, the resolution of 13 voxels was a compromise between

accuracy and computational effort/feasibility.

4 | CONCLUSIONS

This study showed that a universal law (see Equation 3) holds for the

diffusive transport of nutrients, oxygen, and secreted metabolites

through any filamentous fungal pellet. As mentioned above, the

correlation is also known as Archie's law (Archie, 1942) with a ce-

mentation parameter equal to 1.76, which is in the range of porous

rocks (Glover et al., 1997, e.g., determined that the cementation

parameter of sandstone is between 1.5 and 2.5). Strictly speaking,

our law is valid for hyphal fractions less than 0.4 because the max-

imum hyphal fraction of simulated and measured pellets was 0.4.

However, to the best of our knowledge, there are no studies about

filamentous fungi where the measured hyphal fraction is more than

0.4. For example, Cui et al. (1997, 1998) reported average hyphal

F IGURE 7 Correlation factor a for simulated

and experimentally determined pellets. Each datapoint corresponds to the correlation between thehyphal fraction ch and the effective diffusion

factor keff of one pellet, resulting in the fittedexponent a. For each pellet, the fit is based ondiffusion computations through several cubes and

the correlation k c1effa

h= ( − ) . Hyphae ofsimulated pellets are represented with a“resolution” of five (top) and 13 (bottom) voxels indiameter. The increasing resolution decreases the

correlation factor a, and thus the diffusivitydecreases as well. Morphological simulations fordiffusion computations of simulated pellets were

performed with the Monte Carlo methoddescribed in the Section 2. Microcomputedtomography (μCT) measurements for diffusion

computations of experimentally determinedpellets were conducted with a voxel size of 1 μm(three Penicillium chrysogenum, three Aspergillus

niger MF19.5, five A. niger MF22.4, three Rhizopusoryzae pellets), and 2 μm (11 R. stolonifer pellets)[Color figure can be viewed atwileyonlinelibrary.com]

940 | SCHMIDEDER ET AL.

60

fractions between 0.07 and 0.30 for whole A. awamori pellets. If fu-

ture studies are confronted with hyphal fractions more than 0.4, we

propose to fall back on the correlation for randomly orientated

overlapping fibers proposed by Tomadakis and Sotirchos (1991),

which is (as already stated) not very distinct from our correlation.

They were able to show that their correlation was valid for solid

fractions less than 0.6, whereas higher solid fractions resulted in

another correlation. Our law predicts that only one independent

variable, the hyphal fraction (ch), affects pellet diffusivity. Knowing

the profile of the hyphal fraction in pellets, the law k c1eff h1.76= ( − )

determines the mass transport of molecules inside pellets. Molecule

concentrations inside pellets are affected by metabolic rates and the

transport through filamentous mycelia (Celler et al., 2012; Cui et al.,

1998). As the transport can now be calculated, the estimation of

metabolic rates within pellets becomes, for the first time, feasible.

Future experiments should provide information about the morphol-

ogy and metabolic activity or nutrient profiles of pellets, which can

be, for example, measured through flow cytometry or confocal laser

scanning microscopy (Schrinner et al., 2020; Tegelaar et al., 2020;

Veiter & Herwig, 2019). One possibility to determine the distribution

of oxygen and hyphal material inside pellets would be the application

of microelectrodes inside pellets (Hille et al., 2005; Wittier et al.,

1986) followed by μCT measurements (Schmideder, Barthel,

Friedrich, et al., 2019).

This generalized law was deduced from experimental and simu-

lation data. On the one hand, it proved the usefulness and power of

laboratory μCT systems to investigate the natural 3D morphology of

different filamentous fungi in utmost detail. However, as this method

is time and cost intensive and only applicable to a small number of

pellets, the use of Monte Carlo simulations proved to be powerful for

the massive generation of data covering a broad range of morpho-

logical characteristics. This computational approach allowed us to

generate a database of 3125 morphologically different pellets, which

will also open up new avenues of research. Such a database, which

can be accessed by the community, could also open new paths to-

wards parameter estimation of measured pellets of fungal or bac-

terial origin. Conclusions about the evolution of measured pellets

could be deduced because growth and morphological parameters of

simulated pellets are known.

We furthermore anticipate that this contribution will inspire

more sophisticated correlation measurements between morphology

and mass transport in any complex material, for example, in biofilms,

fiber materials, porous media, and fuel cells. In fact, correlations

between the morphology and transport properties (Archie, 1942;

Carman, 1937; Epstein, 1989; Kozeny, 1927) are crucial to compute

transport phenomena in several fields. Exemplarily, correlation laws

for fibrous materials (He et al., 2017; Tamayol et al., 2012; Tomadakis

& Robertson, 2005) are already applied to design nano‐ and micro-

porous membranes (Yuan et al., 2008), heat insulations (Panerai et al.,

2017) and dissipations (Jung et al., 2016), acoustic insulations (Tang

& Yan, 2017), electrodes (Kim et al., 2019), and batteries (Ke et al.,

2018). Concerning fibrous materials, a direct link to our study was

shown (Figure 6). For nonfibrous materials, a combination of 3D

image acquisition, morphological simulations, and mass transport

computations could significantly enhance the understanding of

morphology‐dependent transport phenomena. Hence, we foresee

that the biological and computational approach followed in this study

may be synergistically adopted to other research questions in bio

(techno)logy and beyond.

ACKNOWLEDGMENTS

Special thanks go to Katherina Celler and Gilles P. van Wezel and his

chair who provided the code used in their study (Celler et al., 2012). The

authors thank The Anh Baran for preliminary studies on the morpho-

logical simulations, Clarissa Schulze and Michaela Thalhammer for as-

sistance with μCT measurements, Andrea Pape for preparation of

pellets, Vincent Bürger for the preliminary code for diffusion‐limited

aggregation, and Markus Betz and Christian Preischl for preliminary

studies on diffusion computations. We also wish to thank Christoph

Kirse, Michael Kuhn, Johann Landauer, Thomas Riller, and Johannes

Petermeier for helpful and fruitful discussions. This study made use of

equipment that was funded by the Deutsche Forschungsgemeinschaft

(DFG, German Research Foundation)–198187031. The authors thank

the Deutsche Forschungsgemeinschaft for financial support for this

study within the SPP 1934 DiSPBiotech–315384307 and 315305620

and SPP2170 InterZell–427889137. Open access funding enabled and

organized by Projekt DEAL.

CONFLICTS OF INTEREST

The authors have no conflicts of interest to declare.

AUTHOR CONTRIBUTIONS

Stefan Schmideder did the conception and design of the study. Stefan

Schmideder, Henri Müller, and Lars Barthel wrote the manuscript,

which was edited and approved by all authors. Heiko Briesen and

Vera Meyer supervised the study. Lars Barthel and Ludwig Niessen

cultivated filamentous fungi and prepared pellets for microcomputed

tomography (μCT) measurements. Henri Müller and Stefan Schmi-

deder performed μCT measurements of pellets. Stefan Schmideder,

Henri Müller, and Tiaan Friedrich performed image analysis. Stefan

Schmideder and Tiaan Friedrich set up the code for morphological

Monte Carlo simulations. Stefan Schmideder performed the diffusion

computations and analyzed the results.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the

corresponding author upon reasonable request.

ORCID

Stefan Schmideder http://orcid.org/0000-0003-4328-9724

Henri Müller https://orcid.org/0000-0002-4831-0003

Lars Barthel https://orcid.org/0000-0001-8951-5614

Tiaan Friedrich https://orcid.org/0000-0001-8346-4908

Ludwig Niessen https://orcid.org/0000-0003-4083-2779

Vera Meyer https://orcid.org/0000-0002-2298-2258

Heiko Briesen https://orcid.org/0000-0001-7725-5907

SCHMIDEDER ET AL. | 941

61

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SUPPORTING INFORMATION

Additional supporting information may be found online in the

Supporting Information section.

How to cite this article: Schmideder S, Müller H, Barthel L,

et al. Universal law for diffusive mass transport through

mycelial networks. Biotechnology and Bioengineering. 2021;

118:930–943. https://doi.org/10.1002/bit.27622

SCHMIDEDER ET AL. | 943

63

Supplementary Materials for Paper III: Universal law for

diffusive mass transport through mycelial networks

Fig. S1: Influence of cube size on diffusion computations

Diffusion computations were conducted with different cube sizes of experimentally determined pellets

and three exemplary simulated pellets. 𝑎 value was fitted on base of 𝑘𝑒𝑓𝑓 = (1 − 𝑐ℎ)𝑎, where 𝑘𝑒𝑓𝑓 is

the effective diffusion factor, 𝑐ℎ the hyphal fraction, and a the fitted correlation factor (Schmideder et

al., 2019). Error bars specify the 95% confidence interval. Morphological simulations of pellets were

performed with the Monte Carlo method described in the Methods section. Microcomputed

tomography measurements were conducted with a voxel size of 1 µm (three Penicillium

chrysogenum, three Aspergillus niger MF19.5, five Aspergillus niger MF22.4, three Rhizopus oryzae

pellets) and 2 µm (11 Rhizopus stolonifer pellets). Red circles mark the cube size used for diffusion

computations in the Results section of this study.

64

Fig. S2: Influence of cube size on porosity to determine size of representative elementary

volume (REV)

We investigated the porosity at four positions per pellet. At these positions we altered the cube size and

analyzed the porosity. Analyses were conducted with one pellet per experimentally determined strain

and three exemplary simulated pellets. Morphological simulations of pellets were performed with the

Monte Carlo method described in the Methods section. Microcomputed tomography measurements

were conducted with a voxel size of 1 μm (three Penicillium chrysogenum, three Aspergillus niger

MF19.5, five Aspergillus niger MF22.4, three Rhizopus oryzae pellets) and 2 μm (11 Rhizopus

stolonifer pellets).

65

Fig. S3: Influence of cube size on effective diffusion factor to determine size of representative

elementary volume (REV)

We investigated the effective diffusion factor at four positions per pellet. At these positions we altered

the cube size and analyzed the effective diffusion factor. Analyses were conducted with one pellet per

experimentally determined strain and three exemplary simulated pellets. Morphological simulations of

pellets were performed with the Monte Carlo method described in the Methods section. Microcomputed

tomography measurements were conducted with a voxel size of 1 μm (three Penicillium chrysogenum,

three Aspergillus niger MF19.5, five Aspergillus niger MF22.4, three Rhizopus oryzae pellets) and 2

μm (11 Rhizopus stolonifer pellets).

66

Fig. S4: Comparison of microcomputed tomography (µCT) images of R. stolonifer with a voxel

size of 1 and 2 µm.

Raw and binarised images are exemplary 250 × 250 µm plane cut outs of pellets. The slices of binarised

images are 250 × 250 × 10 µm of the same region as the raw and binarised images. Arrows indicate

exemplary hollow hyphae. Scale bar: 50 µm.

67

Fig. S5: Comparison of correlations between diffusivity and solid fraction.

The correlation proposed by He et al. (2017) and Tomadakis and Sotirchos (1992) were both proposed

for random orientated overlapping fibers. The effective diffusion factors 𝑘𝑒𝑓𝑓 are shown as functions

of the porosity 𝜀, which is defined by the solid/hyphal fraction 𝛷: 𝜀 = 1 − 𝛷.

68

1

Table S1: Parameters for morphological simulations. Parameters with the value ‘user defined’ could

be varied by the user and define all further parameters.

Parameter Symbol Value Unit

Number of spores 𝑁𝑠𝑝 User defined −

Hyphal diameter 𝑑ℎ User defined µ𝑚

Maximum growth angle 𝜃𝑔,𝑚𝑎𝑥 User defined °

Branch angle 𝜃𝑏 User defined °

Branch interval 𝑏 User defined −

Tip extension rate 𝛼𝑡 User defined µ𝑚 ℎ−1

Cultivation period 𝑡𝑒𝑛𝑑 User defined ℎ

Diameter of spores 𝑑𝑠𝑝 1.5 ∙ 𝑑ℎ µ𝑚

Length of germlings 𝑙𝑔𝑒𝑟𝑚 0.5 ∙ 𝑑𝑠𝑝 + 𝑑ℎ µ𝑚

Time step for calculation ∆𝑡 𝑑ℎ

2 𝛼𝑡

ℎ

Length of a segment 𝑙𝑠𝑒𝑔𝑚𝑒𝑛𝑡 𝑑ℎ

2

µ𝑚

Length of apical region 𝑙𝑎𝑝𝑖𝑐𝑎𝑙 𝑏 𝑑ℎ

4

µ𝑚

Length of subapical region 𝑙𝑠𝑢𝑏𝑎𝑝𝑖𝑐𝑎𝑙 𝑏 𝑑ℎ

4

µ𝑚

Minimum mean distance

between two branches

𝑑𝑏,𝑚𝑖𝑛 𝑏 𝑑ℎ µ𝑚

Hyphal diameter in voxels 𝑑ℎ,𝑣𝑥 User defined 𝑣𝑜𝑥

Scaling factor for nodes 𝑓𝑠𝑐𝑎𝑙𝑒 𝑑ℎ,𝑣𝑥

𝑑ℎ

𝑣𝑜𝑥 µ𝑚−1

69

Supplementary Protocol 1: Preparation of pellets

Aspergillus niger Rhizopus stolonifer

Initial cultivation Complete medium (CM) agar Potato extract glucose agar

Spore harvest Add 10 mL physiological salt (PS) solution, scrape spores off with sterile cotton stick and transfer to sterile 15 mL tube. Vortex for 30 s, filter through miracloth filter paper into fresh tube.

Add 10 mL physiological salt (PS) solution, scrape spores off with sterile cotton stick and transfer to sterile 15 mL tube. Vortex for 30 s, filter through miracloth filter paper into fresh tube.

Serial dilution 10-1 in sterile PS solution 10-1 in sterile PS solution

Spore count From 10-1 dilution, Thoma type counting chamber, 0.1 mm chamber depth.

From 10-1 dilution, Thoma type counting chamber, 0.1 mm chamber depth.

Storage of spores 4 °C 4 °C

Pellet production 50 mL CM medium in 250 mL shake flask

100 mL Potato extract glucose medium in 500 mL shake flask

Inoculation 5*106 spores per mL medium 8*102 spores per mL medium

Incubation conditions 250 rpm, 30 °C, 48 h 250 rpm, 23 °C, 48 h

PS solution Sodium chloride 8.9g Add aqua demin. to 1 L Autoclave at 121 °C for 20 min Preparation of CM medium ASP+N (50x), pH 5,5 20 mL Glucose solution (50% (w/v)) 20 mL Magnesium sulfate solution (1 M) 2 mL Trace element solution (1000x) 1 mL Casamino acid solution (10% (w/v)) 10 mL Yeast extract solution (10% (w/v) 50 mL Add aqua demin. to 1 L Autoclave at 121 °C for 20 min Preparation of ASP+N (50x) Potassium chloride 26.1 g Potassium dihydrogen phosphate 74.85 g Sodium nitrate 297.47 g Add aqua demin. to 1 L, pH 5.5 Autoclave at 121 °C for 20 min

70

Preparation of trace element solution (1000x) Zinc sulfate heptahydrate 12.27 g Boric acid 11 g Manganese (II) chloride tetrahydrate 3.15 g Iron (II) sulfate heptahydrate 2.73 g Cobalt (II) chloride hexahydrate 0.92 g Copper (II) sulfate pentahydrate 1.02 g Sodium molybdate dihydrate 1.28 g EDTA 50.85 g Add aqua demin. to 1 L Autoclave at 121 °C for 20 min Preparation of potato extract glucose Potato Extract Glucose Broth (Carl Roth) 26.5g Add aqua demin. to 1 L Autoclave at 121 °C for 20 min

71

Penicillium chrysogenum Rhizopus oryzae

Initial cultivation 3 % malt extract agar (MEA) 3 % MEA

Spore harvest 5 mL sterile tap water, 2 min. homogenization with sterile spatula. Fill to 15 mL sterile Falcon tube and centrifuge 5 min at 5,000 x g. Wash 2x with 5 mL sterile tap water and discard supernatant. Suspend washed conidiospores in 1 mL sterile tap water.

5 mL sterile tap water, 2 min. homogenization with sterile spatula. Fill to 15 mL sterile Falcon tube and centrifuge 5 min at 5,000 x g. Wash 2x with 5 mL sterile tap water and discard supernatant. Suspend washed sporangiospores in 1 mL sterile tap water.

Serial dilution 10-1-10-6 in sterile tap water 10-1-10-6 in sterile tap water

Spore count From 10-2 dilution, Thoma type counting chamber, 0.1 mm chamber depth.

From 10-2 dilution, Thoma type counting chamber, 0.1 mm chamber depth.

Storage of spores 4 °C 4 °C

Pellet production 100 mL pellet production medium for P. chrysogenum

100 mL pellet production medium for Rh. oryzae

Inoculation 104 spores per mL medium 105 spores per mL medium

Incubation conditions 250 rpm, 23 °C, 48 h 250 rpm, 23 °C, 16 h

Preparation of MEA Malt extract 30 g Peptone from soy 3 g Agar 15 g Add aqua demin. to 1 L, pH 5.2 Autoclave at 121 °C for 15 min Preparation of pellet production medium for P. chrysogenum Component 1: Ammoniumsulfat 0.55 % (w/v) autoclave at 121 °C for 15 min Component 2: Difco Yeast Carbon Base 11.7 % (w/v) Glucose 5,5 % (w/v) Filter sterilize though 0.2 µm membrane Mix Component 1: Component 2 9:1 prior to inoculation Preparation of pellet production medium for R. oryzae Glucose 5g Peptone from soy 1.5g Yeast extract 1.4g NaCl 2g K2HPO4 1g Add aqua demin. to 1 L, pH 5.0 Autoclave at 121 °C for 15 min

72

Supplementary Protocol 2:

X-ray microcomputed tomography (µCT) measurements of

filamentous fungal pellets

Equipment

Freeze-dried samples of filamentous fungal pellets (P. chrysogenum, A. niger, R. stolonifer,

and R. oryzae)

X-ray microcomputed tomography system (XCT‐1600HR; Matrix Technologies, Feldkirchen,

Germany)

Sample rod for µCT measurements with a voxel size of 1 µm

Sample rod for µCT measurements with a voxel size of 2 µm, 3 µm, and 4 µm

Self-constructed sample holder A made of polyoxymethylene (POM), in the shape of a

platform

Self-constructed sample holder B made of polyoxymethylene (POM), in the shape of a ton

Self-constructed sample holder C made of polyoxymethylene (POM) and polyimide (PI), in

the shape of a platform (POM) with an attached tube (PI)

Two-component epoxy adhesive(UHU© PLUS sofortfest, Bühl, Germany)

Double-sided tape (Tesa, Norderstedt, Germany)

Procedure

Preparation of P. chrysogenum pellets for µCT measurements with a voxel size of 1 µm:

Double sided tape:

Place a piece of the double-sided tape directly on the sample rod for µCT measurements with

a voxel size of 1 µm.

Place a single P. chrysogenum pellet directly on top of the double-sided tape in a centered

position.

Epoxy adhesive:

Mix the two components of the epoxy adhesive.

Place a drop of the epoxy adhesive on top of the sample rod for µCT measurements with a

voxel size of 1 µm.

Led the adhesive dry for 5 minutes until a solid, but still sticky surface remains.

Place a single P. chrysogenum pellet directly on top of the adhesive in a centered position.

Preparation of A. niger pellets for µCT measurements with a voxel size of 1 µm:

Place the sample holder A on the sample rod for µCT measurements with a voxel size of 1

µm.

Mix the two components of the epoxy adhesive.

Cover the whole top of the sample holder A with a thin layer of the adhesive.

Led the adhesive dry for 5 minutes until a solid, but still sticky surface remains.

Place single or multiple A. niger pellets on top of the adhesive layer in a centered position.

The diameter of all placed pellets together may not be bigger than 2 mm for µCT

measurements with a voxel size of 1 µm

73

Preparation of R. oryzae pellets for µCT measurements with a voxel size of 1 µm:

Place the sample holder B on the sample rod for µCT measurements with a voxel size of 1

µm.

Place single or multiple R. oryzae pellets in the ton (sample holder B) until the ton is filled.

The ton has the size of the field of view of the µCT measurement.

Preparation of R. oryzae and R. stolonifer pellets for µCT measurements with a voxel size of 2, 3, and

4 µm:

Place the sample holder C on the sample rod for µCT measurements with a voxel size of 2, 3,

and 4 µm.

Place single or multiple pellets of R. oryzae or R. stolonifer in the tube (sample holder C) until

the tube is filled. The tube has the size of the field of view of the µCT measurement.

Table 1: Strain, sample holder, and fixation method, used for the pellet preparation for the µCT measurements.

Strain Sample holder Fixation

P. chrysogenum Directly on the sample rod Double-sided tape or epoxy adhesive

A. niger A Epoxy adhesive

R. oryzae; 1 µm voxel size B -

R. oryzae; 2, 3, 4 µm voxel size C -

R. stolonifer C -

µCT measurements:

Perform a dark field and flat field correction of the µCT system for the chosen parameters

before each measurement.

Place the sample rod with the prepared pellets in the manipulator of the µCT system.

Perform a sample rod correction.

Start the µCT measurement with the following parameters:

o For µCT measurements with 1 µm voxel size:

Number of projections: at least 2000

Acceleration voltage: 60 kV

Current: 20 mA

o For µCT measurements with 2, 3, 4 µm voxel size:

Number of projections: 2000

Acceleration voltage: 60 kV

Current: 60 mA

74

6 Discussion

The embedded papers describe developed methods to analyze the detailed three-dimensional

morphology and diffusivity within filamentous fungal pellets. Further, a universal law for the

diffusivity through mycelial networks is proposed based on diffusion computations through

numerous simulated and measured pellets. These methods and findings as well as possible

new paths towards morphological engineering are discussed in the following.

6.1 Morphological analysis of pellets

In the last decades, there has been much progress in macromorphological analysis of pellets

(Table 1 and Sections 2.1.2 and 2.1.3). However, methods to determine the hyphal network,

i.e., the micromorphology, of whole pellets were lacking. Because three-dimensional methods

are required for this purpose, focused beam reflectance measurement, flow cytometry, laser

diffraction, and two-dimensional microscopy are not sufficient (Section 2.1.3). So far, only

confocal laser scanning microscopy (CLSM) was used to visualize three-dimensional hyphal

networks. However, CLSM is limited to a penetration depth of approximately 50 - 150 µm,

and thus, only the periphery (Tegelaar et al., 2020; Villena et al., 2010) or slices of pellets

(Hille et al., 2005, 2009) can be visualized. In addition, these studies missed to analyze the

micromorphology of the visualized 3D hyphal network.

Paper I describes an X-ray microcomputed tomography (µCT) based method to visualize

the micromorphology of whole intact filamentous fungal pellets. This method bridged the

length scale between macroscopic samples, i.e., pellets with a few hundred micrometers in

size, and microscopic inner structures consisting of dense mycelial networks with hyphal di-

ameters down to 3 µm. Three-dimensional image analysis of the µCT measurements revealed

the micromorphology of whole pellets including the location of tips and branches as well as

the total hyphal length. Until today, this was only described for germinating spores and young

dispersed hyphae with the help of two-dimensional image analysis (Figure 2) (Barry et al.,

2015; Cardini et al., 2020; Schmideder et al., 2018). Additionally, the spatial distributions of

the hyphal fraction, tip and branch density, and HGU were determined within whole intact

pellets (Paper I). The spatial distribution of the hyphal fraction provided new insights into the

symmetry of fungal pellets. Further, hypotheses with respect to their development can be de-

duced. Analyzed A. niger pellets (Paper I, II, and III) showed almost spherical symmetry and

a dense center, which are strong indicators for the pellet formation being of coagulative type

(Veiter et al., 2018; Zhang and Zhang, 2016). P. chrysogenum pellets (Paper I and III) showed

no spherical symmetry and a couple of dense regions which could be caused by their hyphal

element agglomeration pellet formation type (Veiter et al., 2018). Contrary, R. stolonifer pel-

75

lets (Paper III) showed a homogeneous spatial distribution of the hyphal fraction, which is an

indicator for non-coagulative pellet formation (Cairns et al., 2019b; Žnidaršic et al., 1998).

The developed method to analyze pellets based on µCT measurements has significant ad-

vantages compared to established methods. Most importantly, it is the only approach to an-

alyze the micromorphology of whole intact pellets. Contrary to pellet slicing (Hille et al.,

2005; Priegnitz et al., 2012), µCT measurements offer a nondestructive technique to visualize

microscopic structures (Salvo et al., 2003; Stock, 2009), which was proven for filamentous

fungi in Paper I. With freeze-drying, sample preparation is rather simple, especially com-

pared to fluorescent staining for CLSM measurements (Hille et al., 2009; Veiter and Herwig,

2019) and/or pellet slicing (Hille et al., 2005; Priegnitz et al., 2012). However, every method

has its limitations. Due to restricted measurement volumes and long measurement times, the

number of investigated pellets in the presented studies was low. Depending on the size of the

pellets and the required settings of the applied laboratory µCT system (XCT1600HR; Matrix

Technologies, Feldkirchen, Germany), the measurement of 1 - 10 pellets took 1.5 - 4 hours.

Additionally, the resolution of µCT systems can be restricting. While hyphal diameters of fila-

mentous fungi range between 2 - 10 µm (Lehmann et al., 2019; Meyer et al., 2020), hyphae of

filamentous bacteria often have diameters smaller than 1 µm (Zacchetti et al., 2018). Because

the minimum voxel size with a sufficient signal to noise ratio of the applied laboratory µCT

system is 1 µm, the hyphal network of the filamentous bacterium Lentzea aerocolonigenes

(Schrinner et al., 2020) could not be visualized. However, pellets of two common filamentous

fungal cell factories, Aspergillus niger and Penicillium chrysogenum, have been analyzed in

Paper I. Paper III showed that Rhizopus stolonifer and Rhizopus oryzae pellets can also be

visualized with the applied µCT system.

It is conceivable to adapt the developed image analysis pipeline in Paper I to CLSM mea-

surements of dispersed hyphae and the periphery or slices of pellets. Because CLSM is often

available in laboratories working with filamentous fungi, this could strongly contribute to

three-dimensional morphological analyses. To overcome the limitation of the small number

of analyzed pellets, synchrotron measurements can be applied in the future. As proposed in

a conference contribution (Müller et al., 2020), synchrotron measurements were recently ap-

plied to visualize thousands of pellets to track the development and heterogeneity of A. niger

pellets during a shake flask cultivation. However, the results of these measurements are not

part of this thesis. Measurements with synchrotron or high-end laboratory µCT systems will

also shift restrictions concerning image resolution. Thus, pellets of filamentous bacteria with

hyphae thinner than 1 µm might be measured and analyzed in future studies.

The ability to determine the three-dimensional microscopic structure of pellets enabled

the computation of the effective diffusion through filamentous fungal networks (Section 6.2).

Further, this method will open new paths towards morphological engineering to increase the

productivity of pellets (Section 6.3).

76

6.2 Diffusive transport through mycelial networks

The transport of nutrients and oxygen into pellets is mainly driven by diffusion and limited

by the dense hyphal network (Cairns et al., 2019b; Hille et al., 2005; Veiter et al., 2018). As

a result, the concentrations of oxygen and nutrients decrease towards the center of pellets

(Cronenberg et al., 1994; Hille et al., 2005), which can reduce growth and metabolic activity

(Cairns et al., 2019b; Veiter et al., 2018). While correlation laws between transport properties

and three-dimensional structures of fibrous materials are already used to design membranes

(Yuan et al., 2008), heat insulations (Panerai et al., 2017), acoustic insulations (Tang and Yan,

2017), electrodes (Kim et al., 2019), and batteries (Ke et al., 2018), such laws do not exist for

filamentous microorganisms. A correlation between the diffusivity and the micromorphology

of hyphal networks can be harnessed to compute the diffusion of nutrients, oxygen, and se-

creted metabolites through filamentous pellets, and thus, contribute to the rational design of

pellet morphologies.

Paper II describes the only method to date to correlate the microscopic structure and the

effective diffusivity of filamentous fungi. This method is based on diffusion computations

through three-dimensional hyphal networks. To reveal a universal law for filamentous fungi,

diffusion computations were conducted through structures gained from three-dimensional

µCT measurements of 66 fungal pellets and 3125 Monte Carlo simulated pellets that consid-

ered the broad morphological range of filamentous microorganisms (Paper III). Depending

on the size of the pellets, approximately 50 – 150 representative cubic sub-volumes per pellet

were extracted and further used to compute the geometrical diffusion hindrance keff . Corre-

lating keff with the hyphal fraction ch (similar to solid fraction), the data showed an excellent

fit to the following equation:

keff = (1 − ch)1.76 . (6.1)

Because keff is independent from the diffusing component i (Becker et al., 2011) and the

diffusion coefficient of the bulk medium Di,bulk can be estimated from medium conditions

(Yaws, 2014), keff determines the effective diffusion coefficient Di,eff (Equation 2.3), and

thus, the diffusive mass transport of molecules through pellets. Equation 6.1 unveils that

only one independent variable, the hyphal fraction (ch), affects the diffusivity through hyphal

networks. Contrary, micromorphological parameters such as growth angles, branch angles,

hyphal diameters, branching frequency, and number of initial spores do not influence the

diffusion hindrance (Paper III).

The presented correlation (Equation 6.1) is not very distinct from the law of randomly ori-

entated overlapping fibers by Tomadakis and Sotirchos (1991) and similar to Archie’s law

(Archie, 1942) with a cementation parameter equal to 1.76. Contrary, the suggested corre-

lation uncovered discrepancies with assumptions made in morphological modeling of pellets

(Buschulte, 1992; Celler et al., 2012; Cui et al., 1998; Lejeune and Baron, 1997; Meyerhoff

et al., 1995). However, these studies lacked reasonable mechanistic or empirical derivations

of the effective diffusivity. Until today, Cronenberg et al. (1994) and Hille et al. (2009) con-

ducted probably the most extensive experiments to determine the effective diffusivity through

77

inactivated pellets by stimulus response measurements of the oxygen concentration. While

they obtained comparable effective diffusion factors as in Paper II and III, they did not quan-

tify the corresponding micromorphology reasonably.

To validate the accuracy of the diffusion computations, the solutions for parallel nonover-

lapping fibers (Perrins et al., 1979; Tomadakis and Sotirchos, 1991) and for randomly ori-

entated overlapping straight fibers (Tomadakis and Sotirchos, 1991) were compared with the

computed diffusivities through such structures (Paper II and III). Because image resolution

can influence computed properties (Velichko et al., 2009), simulated structures were varied

in resolution, i.e., the diameter of the fibers were represented with a different number of vox-

els. The diffusion computations with high resolutions (fibers represented with more than 10

voxels in diameter) showed a high accuracy, whereas computations through images with low

resolutions resulted in a slight underestimation of the diffusivity (Paper II and III). As the

image resolution of µCT measurements was restricted, hyphae were represented with approx-

imately 4 - 5 voxels in diameter. Thus, computed diffusivities might be slightly underesti-

mated (Paper II and III). The cementation parameters of measured P. chrysogenum, A. niger,

R. stolonifer, and R. oryzae pellets were comparable to the mean cementation parameter of

3125 simulated pellets with a resolution to represent hyphae with 5 voxels in diameter. To

achieve a high accuracy, the diffusion computations were also conducted through the 3125

simulated pellets with a resolution of 13 voxels. As a result, the universal law (Equation 6.1)

was obtained.

The diffusion computations through numerous measured and simulated pellets spanning

the broad morphological range of filamentous fungi suggest that the determined correlation

(Equation 6.1) is universal for filamentous fungi. Because the micromorphology of filamen-

tous bacteria was also considered in the simulations, this correlation might also be applicable

to them.

To determine the universal law, the radial diffusivity was investigated (Paper III), i.e., the

direction of the diffusion pointed to the center of pellets. However, possible anisotropic be-

haviors of filamentous pellets could alter the diffusivity. Contrary to simulated pellets, mea-

sured pellets showed a slight anisotropy, which has been discussed for one A. niger strain

(MF22.4) in Paper II. For this strain, diffusivity in tangential direction was slightly lower

compared to the radial direction. While the universal diffusion law of Paper III can be applied

to isotropic pellets, diffusion computations (Paper II) should be conducted to determine the

diffusion behavior of strongly anisotropic pellets.

The combination of three-dimensional image acquisition, morphological simulations, and

diffusion computations significantly enhanced the understanding of morphology-dependent

transport phenomena. Because the determined effective diffusion factor ke f f (Paper II and III)

is the inverse of the formation factor, it can be also used to describe the conductivity or per-

meability of porous media (Tomadakis and Robertson, 2005). Hence, the described method-

ology for filamentous fungi is transferable to other research questions in bio(techno)logy and

beyond.

78

The described methods and findings enable the correlation between microscopic structures

and diffusivities of filamentous fungal networks. This knowledge will contribute to engineer

the morphology of pellets to reach a desired nutrient supply resulting in an increased product

formation.

6.3 New paths towards morphological engineering

The morphology of filamentous fungi has a strong influence on their productivity. Thus, mor-

phological engineering is a key in filamentous fungal biotechnology (Cairns et al., 2019b;

Krull et al., 2013). To understand and control the morphogenesis of filamentous pellets, it

is essential to analyze their hyphal networks and to know the diffusive barrier for nutrients,

oxygen, and secreted metabolites. Because the embedded Paper I - III enable the micromor-

phological analysis of whole pellets and propose a universal diffusion law, new paths towards

morphological engineering of filamentous pellets will be opened. The following paragraphs

present a few examples of prospects concerning experimental and modeling approaches.

Experimental approaches suggest numerous opportunities for morphological engineering.

For example, genetic approaches aim to alter morphological properties (Cairns et al., 2019b)

such as the branching frequency (Fiedler et al., 2018; He et al., 2016). Process engineering

approaches often have the goal to alter the spatial distribution of the hyphal fraction within

pellets (Lin et al., 2010). So far, analyzing the outcome of these engineering approaches with

respect to the inner morphology of pellets was limited to qualitative statements about the spa-

tial distribution of the hyphal fraction (Hille et al., 2005, 2009; Lin et al., 2010; Priegnitz et al.,

2012). Now, µCT measurements and subsequent image analysis enable the characterization

of the micromorphology within whole pellets. Thus, the outcome of experimental approaches

can be investigated in unprecedented detail.

Modeling approaches deepen a mechanistic understanding of the morphogenesis of pellets.

Although several useful models to simulate the development of the morphology and nutrient

supply in pellets exist, most of them lack suitable experimental input about the inner structure

and diffusivity of pellets. The microscopic and continuum pellet models described in Sec-

tion 2.3.2 consider spatial distributions of morphological properties. For these approaches,

the developed µCT based method (Paper I) can provide morphological data to an unprece-

dented extent. Additionally, many morphological modeling approaches include the diffusive

mass transport of nutrients and oxygen through the hyphal network (Buschulte, 1992; Celler

et al., 2012; Lejeune and Baron, 1997; Meyerhoff et al., 1995). Based on the suggested uni-

versal law for the diffusivity of filamentous fungal networks (Paper III), the required effective

diffusion coefficient can be calculated. Hence, the validation and improvement of existing

models through the use of micromorphological data and laws for the diffusivity through hy-

phal networks can be achieved.

The concentration of molecules such as nutrients, oxygen, and secreted metabolites within

pellets are affected by metabolic rates and the transport through the hyphal network (Celler

et al., 2012; Cui et al., 1998). Because the transport can now be calculated (Paper II and III),

79

the estimation of metabolic rates within pellets will become feasible. To estimate metabolic

rates, experiments should provide information about the spatial distribution of molecules and

morphological properties within pellets. For example, the application of microelectrodes

within pellets (Cronenberg et al., 1994; Hille et al., 2009) followed by µCT measurements

(Paper I) would provide the spatial distribution of oxygen and (micro)morphological proper-

ties within pellets. Based on partial differential diffusion-reaction equations that are already

proposed in several modeling approaches (Buschulte.1992, King.1998, Celler.2012), the es-

timation of oxygen consumption rates might then be conducted. The described procedure

might also be used to determine metabolic rates of other substances including nutrients and

secreted metabolites.

The product of interest determines whether a saturation or a limitation of nutrients inside

fungal pellets is pursued (Veiter et al., 2018). Thus, optimal pellet morphologies cannot be

generalized in bioprocesses (Krull et al., 2010). In Figure 5, an idealized workflow for the

construction of pellets as optimized production hosts is proposed, which is based on a sketch

in Paper II. The first step of this workflow is the generation of a database consisting of numer-

ous pellet structures. The database might consist of both µCT measured and simulated pellets.

Further, partial differential diffusion-reaction equations (Buschulte, 1992; Celler et al., 2012;

King, 1998) should be applied to compute substrate-limited and substrate-saturated regions

of each pellet of the database. For the reaction term, substrate consumption rates have to be

acquired from literature or experiments. The spatial distribution of the hyphal fraction (from

database) and the universal diffusion law described in Paper III determine the diffusion term.

Depending on whether substrate limitation or saturation is desired, a suitable pellet structure

can be selected from the database. Based on process and/or genetic engineering approaches,

the chosen pellet structure should then be realized in bioreactors. Although there have been

many advances in morphological engineering, the realization of suitable pellets is most likely

going to be an iterative process. For this, a detailed verification of the pellet morphology

can be conducted based on µCT measurements and 3D image analysis. Obviously, some of

the proposed steps of the idealized workflow have to be investigated and elaborated in much

more detail. However, this workflow shows that the developed methods and findings embed-

ded in this thesis are important steps towards the construction of filamentous fungal pellets as

optimized production hosts.

So far, this dissertation mainly addressed individual pellets. However, submerged cultures

of filamentous microorganisms can result in broad pellet size distributions (Kurt et al., 2018;

Schrinner et al., 2020) influencing the further growth and production behavior (King, 1998;

Wösten et al., 2013) as well as the rheology and mass transfer in the bioprocess (Bliatsiou

et al., 2020). Contrary to the microscopic and continuum models elaborated in Section 2.3.2,

population balance equations (PBEs) allow the modeling of the development of the mor-

phological heterogeneity (King, 1998). On the one hand, recent advances in measuring the

macromorphology of numerous pellets (Sections 2.1.2 and 2.1.3) might contribute to PBEs

that describe the development of the size distribution (Edelstein and Hadar, 1983; Tough

et al., 1995). On the other hand, micromorphological data lacks as input of future PBEs with

80

Figure 5: Idealized workflow for the construction of filamentous fungal pellets as optimizedproduction hosts.

81

a high structuredness. As proposed in Schmideder et al. (2018), population balance models

with a high structuredness can consider several morphological properties including the size

of pellets, the diameter of the shell layer supplied with oxygen, the total length of active and

inactive hyphae, and the total number of growing tips. The location of tips and hyphal mate-

rial can be determined based on µCT measurements and subsequent image analysis (Paper I).

While laboratory µCT systems enable the visualization of a few pellets with one measurement,

hundreds of pellets can be visualized based on synchrotron radiation within a few minutes

(Section 6.1). Further, active and inactive regions of pellets can be estimated based on exper-

imental approaches (Section 2.2.2) or diffusion-reaction equations (Celler et al., 2012; King,

1998). Thus, PBEs with a high morphological structuredness can be developed through the

use of micromorphological data (Paper I) and the proposed universal diffusion law (Paper III).

Such modeling approaches will deepen the mechanistic understanding of the development of

(pellet) heterogeneities including growth, breakage, and aggregation processes.

To conclude, the developed methods to determine the micromorphology (Paper I) and effec-

tive diffusivity (Paper II) of pellets and the universal diffusion law through hyphal networks

(Paper III) will open new paths towards morphological engineering to enhance productivities

in filamentous fungal biotechnology.

82

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8 Appendix: List of Publications

Peer-Reviewed Publications

Stefan Schmideder, Christoph Kirse, Julia Hofinger, Sascha Rollié, and Heiko Briesen,

2018, Modeling the separation of microorganisms in bioprocesses by flotation. Pro-

cesses, 6(10): 184.

Stefan Schmideder, Lars Barthel, Tiaan Friedrich, Michaela Thalhammer, Tijana Ko-

vacevic, Ludwig Niessen, Vera Meyer, and Heiko Briesen, 2019, An X-ray microtomography-

based method for detailed analysis of the three-dimensional morphology of fungal pel-

lets. Biotechnology and Bioengineering, 116(6): 1355–1365.

Stefan Schmideder, Lars Barthel, Henri Müller, Vera Meyer, and Heiko Briesen, 2019,

From three-dimensional morphology to effective diffusivity in filamentous fungal pel-

lets. Biotechnology and Bioengineering, 116(12): 3360–3371.

Kathrin Schrinner, Lukas Veiter, Stefan Schmideder, Philipp Doppler, Marcel Schrader,

Nadine Münch, Kristin Althof, Arno Kwade, Heiko Briesen, Christoph Herwig, and

Rainer Krull, 2020, Morphological and physiological characterization of filamentous

Lentzea aerocolonigenes: Comparison of biopellets by microscopy and flow cytome-

try. PLOS ONE, 15(6): e0234125.

Stefan Schmideder, Henri Müller, Lars Barthel, Tiaan Friedrich, Ludwig Niessen,

Vera Meyer, and Heiko Briesen, 2021, Universal law for diffusive mass transport through

mycelial networks. Biotechnology and Bioengineering, 118(2):930–943.

Oral Presentations

Stefan Schmideder, Christoph Kirse, Julia Hofinger, Sascha Rollié, and Heiko Briesen,

2018, Modeling the separation of microorganisms in bioprocesses by flotation. 6th

Population Balance Modelling Conference (PBM 2018), Gent, Belgium.

Kathrin Pommerehne, Marcel Schrader, Chrysoula Bliatsiou, Stefan Schmideder, Lutz

Böhm, Heiko Briesen, Matthias Kraume, Arno Kwade, and Rainer Krull1, 2018, Ex-

perimental and numerical investigations on cultivations of filamentous microorgan-

isms towards a better understanding and process control. ProcessNet Jahrestagung und

DECHEMA-Jahrestagung der Biotechnologen 2018, Aachen, Germany.

91

Heiko Briesen, Stefan Schmideder, Henri Müller, 2020, Morphological characteriza-

tion and modeling of filamentous fungi. 4th Indo-German Workshop on Advances in

Materials, Reaction & Separation Processes, Berlin, Germany.

Stefan Schmideder, Lars Barthel, Henri Müller, Vera Meyer, and Heiko Briesen, 2020,

On the three-dimensional morphology and substrate-diffusion in filamentous fungal

pellets. 15th European Conference on Fungal Genetics (ECFG15), Rome, Italy.

Stefan Schmideder, Lars Barthel, Henri Müller, Vera Meyer, and Heiko Briesen, 2020,

From macro- to micro-morphological properties of filamentous fungal pellets. Pro-

cessNet Jahrestagung und DECHEMA-Jahrestagung der Biotechnologen 2020, Web-

Konferenz.

Poster Presentations

Stefan Schmideder, Tiaan Friedrich, Tijana Kovacevic, Lars Barthel, Philipp Kunz,

Vera Meyer, Rudibert King, and Heiko Briesen, 2018, Growth of filamentous microor-

ganisms: PBM and experimental determination of rate equations. 6th Population Bal-

ance Modelling Conference (PBM 2018), Gent, Belgium.

Lars Barthel, Stefan Schmideder, Heiko Briesen, and Vera Meyer, 2019, An X-ray

microtomography-based method for detailed analysis of the three-dimensional mor-

phology of fungal pellets: Aspergillus niger as a case study. Molecular Biology of

Fungi (MBF 2019), Göttingen, Germany.

Henri Müller, Stefan Schmideder, Lars Barthel, Ludwig Niessen, Vera Meyer, and

Heiko Briesen, 2020, Optimized X-ray microcomputed tomography and 3D volumetric

image processing of filamentous fungal pellets. ProcessNet Jahrestagung und DECHEMA-

Jahrestagung der Biotechnologen 2020, Web-Konferenz.

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